Finite Group DatabasebetaFinite Group Databasebeta| order | 24448 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C191 · Schur multiplier (H2) = C22 |
| direct product | #2110×C191 |
| subgroup | G/H | |
|---|---|---|
| center | C8×C191 | C42 |
| commutator | C4 | C2×C42×C191 |
| Frattini, cosocle | C2×C8 | C23×C191 |
| socle | C2×C191 | C2×#97 |
| prime radical | C23×C191 | M16 |
| LCS | G ▷ C4 ▷ C1 | |
| UCS | C1 ◁ C8×C191 ◁ G | |
160 conjugacy classes of subgroups.
| minimal degree | μ(G) = 223 |
| transitive degree | μt(G) = 6112 |
A minimal faithful permutation representation — 3 generators on 223 points:
(1,2,4,8,5,10,16,24,6,9,17,23,18,25,31,32)(3,11,13,27,14,20,29,22,12,26,15,30,28,7,19,21)(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);(1,3)(2,7,9,20)(4,15)(5,14)(6,12)(8,22,23,21)(10,11,25,26)(13,17)(16,19)(18,28)(24,30,32,27)(29,31);(3,12)(7,20)(11,26)(13,15)(14,28)(19,29)(21,22)(27,30)8404 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24448, 842);