Finite Group DatabasebetaFinite Group Databasebeta| order | 12948 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊(C83⋊#261) |
| unambiguous semidirect product | C83⋊(C3⋊#261) |
| Fitting, socle, derived, Hall | C3×C13×C83 ⋊ C4 |
| Hall | C13×C83 ⋊ Dic3 |
| Hall | C3×C83 ⋊ #261 |
| Sylow | C83 ⋊ C3⋊#261 |
| Hall | C3×C13 ⋊ Dic83 |
| Sylow | C13 ⋊ Dic249 |
| Sylow | C3 ⋊ C83⋊#261 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C13×C83 | C4 |
| prime radical, cosocle | C3×D13×C83 | C2 |
| LCS | G ▷ C3×C13×C83 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
| minimal degree | μ(G) = 99 |
| transitive degree | μt(G) = 3237 |
A minimal faithful permutation representation — 2 generators on 99 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)(85,86,87,89)(88,91,92,93)(90,95,96,94)(98,99);(1,2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,48,50,52,54,56,58,60,62,64,66,68,70,72,74,76,78,80,82,83,81,79,77,75,73,71,69,67,65,63,61,59,57,55,53,51,49,47,45,43,41,39,37,35,33,31,29,27,25,23,21,19,17,15,13,11,9,7,5,3)(84,85,88,93,95,86,90,96,89,94,91,92,87)(97,98,99)Polycyclic presentation:
2^2,3,13,83|a^2=b,c^a=c^2,d^a=d^5,e^a=e^82,d^b=d^12999 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12948, 25);