Finite Group DatabasebetaFinite Group Databasebeta| order | 24448 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| dihedral | D12224 |
| Fitting | C64×C191 ⋊ C2 |
| Sylow | C191 ⋊ D64 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | D6112 |
| commutator, cosocle | C32×C191 | C22 |
| Frattini | C32 | C2×D191 |
| Fitting | C64×C191 | C2 |
| socle | C2×C191 | D32 |
| hypercenter | C64 | D191 |
| hypocenter | C191 | D64 |
| LCS | G ▷ C32×C191 ▷ C16×C191 ▷ C8×C191 ▷ C4×C191 ▷ C2×C191 ▷ C191 | |
| UCS | C1 ◁ C2 ◁ C4 ◁ C8 ◁ C16 ◁ C32 ◁ C64 | |
40 conjugacy classes of subgroups.
| minimal degree | μ(G) = 255 |
| transitive degree | μt(G) = 12224 |
A minimal faithful permutation representation — 2 generators on 255 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64)(65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255);(2,64)(3,63)(4,62)(5,61)(6,60)(7,59)(8,58)(9,57)(10,56)(11,55)(12,54)(13,53)(14,52)(15,51)(16,50)(17,49)(18,48)(19,47)(20,46)(21,45)(22,44)(23,43)(24,42)(25,41)(26,40)(27,39)(28,38)(29,37)(30,36)(31,35)(32,34)(66,255)(67,254)(68,253)(69,252)(70,251)(71,250)(72,249)(73,248)(74,247)(75,246)(76,245)(77,244)(78,243)(79,242)(80,241)(81,240)(82,239)(83,238)(84,237)(85,236)(86,235)(87,234)(88,233)(89,232)(90,231)(91,230)(92,229)(93,228)(94,227)(95,226)(96,225)(97,224)(98,223)(99,222)(100,221)(101,220)(102,219)(103,218)(104,217)(105,216)(106,215)(107,214)(108,213)(109,212)(110,211)(111,210)(112,209)(113,208)(114,207)(115,206)(116,205)(117,204)(118,203)(119,202)(120,201)(121,200)(122,199)(123,198)(124,197)(125,196)(126,195)(127,194)(128,193)(129,192)(130,191)(131,190)(132,189)(133,188)(134,187)(135,186)(136,185)(137,184)(138,183)(139,182)(140,181)(141,180)(142,179)(143,178)(144,177)(145,176)(146,175)(147,174)(148,173)(149,172)(150,171)(151,170)(152,169)(153,168)(154,167)(155,166)(156,165)(157,164)(158,163)(159,162)(160,161)Polycyclic presentation:
2^7,191|c^2=de,d^2=ef,e^2=fg,f^2=g,b^a=bc,c^a=cd,d^a=de,e^a=ef,f^a=fg,h^a=h^190,c^b=cd,d^b=de,e^b=ef,f^b=fg,h^b=h^1906115 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24448, 2723);