Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C13 · Schur multiplier (H2) = C8 |
| direct product | C13×#8270 |
| subgroup | G/H | |
|---|---|---|
| center | C42×C13 | C2×D4 |
| commutator | C2×C4 | C2×C42×C13 |
| Frattini, cosocle | C2×C42 | C23×C13 |
| socle | C22×C13 | C4×C4⋊C4 |
| prime radical | C23×C13 | #117 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C42×C13 ◁ C2×C4×C8×C13 ◁ G | |
342 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 832 |
A minimal faithful permutation representation — 3 generators on 45 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(15,19,21,24)(20,26,27,28)(30,31)(32,35)(33,37)(34,36)(38,42)(39,41)(40,43)(44,45);(14,15)(16,20)(17,24)(18,21)(19,25)(22,28)(23,27)(26,29)(30,32,33,38,34,39,40,44)(31,35,37,42,36,41,43,45);(14,16,17,22,18,23,25,29)(15,20,24,28,21,27,19,26)(31,36)(35,41)(37,43)(42,45)988 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 1258);