Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C13 · Schur multiplier (H2) = C29 |
| direct product | C13×#61105 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C13 | D42 |
| commutator, Frattini, cosocle | C2×C4 | C25×C13 |
| socle | C2×C13 | C2×D42 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C13 ◁ C22×C4×C13 ◁ G | |
2620 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 416 |
A minimal faithful permutation representation — 5 generators on 45 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15)(16,26)(17,28)(18,23)(19,24)(20,37)(21,25)(22,31)(27,43)(29,32)(30,44)(33,45)(34,40)(35,41)(36,42)(38,39);(14,16)(15,17)(18,33)(19,28)(20,29)(21,22)(23,39)(24,31)(25,32)(26,37)(27,34)(30,41)(35,38)(36,44)(40,45)(42,43);(14,17)(15,22)(16,25)(18,30)(19,31)(20,26)(21,32)(23,38)(24,29)(27,42)(28,37)(33,40)(34,39)(35,43)(36,45)(41,44);(14,18)(15,23)(16,27)(17,30)(19,34)(20,35)(21,36)(22,38)(24,40)(25,42)(26,43)(28,44)(29,33)(31,39)(32,45)(37,41);(14,19,21,20)(15,24,25,37)(16,28,22,29)(17,31,32,26)(18,34,36,35)(23,40,42,41)(27,44,38,33)(30,39,45,43)754 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 54093);