Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C13 · Schur multiplier (H2) = C24 |
| direct product | C13×#17968 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C13 | C22×D4 |
| commutator | C2×C4 | C23×C4×C13 |
| Frattini, cosocle | C42 | C24×C13 |
| socle | C22×C13 | C2×C4×D4 |
| prime radical | C13×#3171 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C13 ◁ C13×#431 ◁ G | |
622 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 1664 |
A minimal faithful permutation representation — 4 generators on 45 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15)(16,20)(17,19)(18,22)(21,25)(23,27)(24,26)(28,29)(30,31,34,38,35,32,39,37)(33,36,42,44,41,40,45,43);(15,19)(17,25)(20,26)(21,22)(24,29)(27,28)(30,32)(31,35)(33,40)(34,37)(36,41)(38,39)(42,43)(44,45);(14,16)(15,20)(17,24)(18,23)(19,26)(21,28)(22,27)(25,29)(30,33,34,42,35,41,39,45)(31,36,38,44,32,40,37,43);(16,23)(20,27)(24,29)(26,28)(31,32)(33,41)(37,38)(42,45)832 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 10956);