Finite Group DatabasebetaFinite Group Databasebeta| order | 13184 |
| automorphism | ? |
| homology | Abelianization (H1) = C128 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C103⋊C128 |
| derived, Sylow | C103 ⋊ C128 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C64 | D103 |
| commutator, hypocenter | C103 | C128 |
| Fitting, cosocle | C64×C103 | C2 |
| socle, prime radical | C2×C103 | C64 |
| LCS | G ▷ C103 | |
| UCS | C1 ◁ C64 | |
16 conjugacy classes of subgroups.
| minimal degree | μ(G) = 231 |
| transitive degree | μt(G) = 13184 |
A minimal faithful permutation representation — 2 generators on 231 points:
(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)(104,105,106,112,107,113,118,133,108,114,119,134,123,138,148,168,109,115,120,135,124,139,149,169,127,142,152,172,158,178,188,203,110,116,121,136,125,140,150,170,128,143,153,173,159,179,189,204,130,145,155,175,161,181,191,206,164,184,194,209,198,213,218,224,111,117,122,137,126,141,151,171,129,144,154,174,160,180,190,205,131,146,156,176,162,182,192,207,165,185,195,210,199,214,219,225,132,147,157,177,163,183,193,208,166,186,196,211,200,215,220,226,167,187,197,212,201,216,221,227,202,217,222,228,223,229,230,231);(1,2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,48,50,52,54,56,58,60,62,64,66,68,70,72,74,76,78,80,82,84,86,88,90,92,94,96,98,100,102,103,101,99,97,95,93,91,89,87,85,83,81,79,77,75,73,71,69,67,65,63,61,59,57,55,53,51,49,47,45,43,41,39,37,35,33,31,29,27,25,23,21,19,17,15,13,11,9,7,5,3)Polycyclic presentation:
2^7,103|a^2=b,b^2=c,c^2=d,d^2=e,e^2=f,f^2=g,h^a=h^1023392 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13184, 2329);