Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C13 · Schur multiplier (H2) = C28×C4 |
| direct product | C13×#60643 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C13 | C22×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C13 |
| socle | C22×C13 | C23×D4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C13 ◁ C2×C13×#117 ◁ G | |
3194 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 832 |
A minimal faithful permutation representation — 5 generators on 49 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(15,17)(18,19)(20,29)(21,26)(22,27)(23,37)(24,28)(25,32)(30,42)(31,39)(33,43)(34,40)(35,41)(36,47)(38,46)(44,49)(45,48);(18,20,23,32,24,33,22,31)(19,25,27,29,28,39,37,43)(21,30,36,46,34,44,35,45)(26,38,41,42,40,48,47,49);(14,15,16,17)(18,21)(19,26)(20,30)(22,35)(23,36)(24,34)(25,38)(27,41)(28,40)(29,42)(31,45)(32,46)(33,44)(37,47)(39,48)(43,49);(21,34)(26,40)(30,44)(35,36)(38,48)(41,47)(42,49)(45,46);(18,22,24,23)(19,27,28,37)(20,31,33,32)(21,35,34,36)(25,29,39,43)(26,41,40,47)(30,45,44,46)(38,42,48,49)832 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 53631);