Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C13 · Schur multiplier (H2) = C23×C4 |
| direct product | C13×#10890 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C13 | #386 |
| commutator | C2×C4 | C2×C42×C13 |
| Frattini, cosocle | C23×C4 | C23×C13 |
| socle | C2×C13 | #1436 |
| prime radical | C24×C13 | #41 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C13 ◁ C23×C4×C13 ◁ G | |
676 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 416 |
A minimal faithful permutation representation — 3 generators on 45 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,19,23,20,24,18,32)(16,25,29,35,28,40,27,21)(17,22,30,37,31,38,33,36)(26,41,42,34,43,39,44,45);(14,16)(15,21,24,35)(17,26)(18,27)(19,29)(20,28)(22,34,38,45)(23,25,32,40)(30,42)(31,43)(33,44)(36,41,37,39);(14,17,19,30,20,31,18,33)(15,22,23,37,24,38,32,36)(16,26,29,42,28,43,27,44)(21,34,25,39,35,45,40,41)754 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 3878);