Finite Group DatabasebetaFinite Group Databasebeta| order | 13184 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Fitting | #560×C103 ⋊ C2 |
| Sylow | C103 ⋊ #3529 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D103 |
| commutator, socle, cosocle | C22×C103 | C25 |
| Fitting | #560×C103 | C2 |
| hypercenter | #560 | D103 |
| hypocenter | C103 | #3529 |
| LCS | G ▷ C22×C103 ▷ C103 | |
| UCS | C1 ◁ C22 ◁ #560 | |
1058 conjugacy classes of subgroups.
| minimal degree | μ(G) = 127 |
| transitive degree | μt(G) = 3296 |
A minimal faithful permutation representation — 5 generators on 127 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)(112,115,116,123)(113,119,118,125)(114,122,121,127)(117,124,120,126);(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)(105,109)(108,111)(113,118)(114,121)(119,125)(122,127);(105,109)(106,110)(114,121)(117,120)(122,127)(124,126);(104,106)(105,108)(107,110)(109,111)(112,114)(113,117)(115,122)(116,121)(118,120)(119,124)(123,127)(125,126);(104,105)(106,108)(107,109)(110,111)(112,113)(114,120)(115,119)(116,118)(117,121)(122,126)(123,125)(124,127)Polycyclic presentation:
2^7,103|e^2=f,b^a=bf,c^a=cg,d^a=dfg,c^b=cfg,d^b=df,h^e=h^1021007 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13184, 18645);