Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C13 · Schur multiplier (H2) = C24 |
| direct product | C13×#33428 |
| subgroup | G/H | |
|---|---|---|
| center | C8×C13 | #117 |
| commutator | C2×C4 | C23×C4×C13 |
| Frattini, cosocle | C2×C8 | C24×C13 |
| socle | C2×C13 | C2×#432 |
| prime radical | C2×C13×#41 | C2×C4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C8×C13 ◁ C13×#405 ◁ G | |
528 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 416 |
A minimal faithful permutation representation — 4 generators on 45 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,17,23,18,24,30,41,19,22,31,37,32,38,44,45)(16,25,27,39,28,35,43,40,26,20,29,33,42,21,34,36);(14,16)(15,20)(17,29)(18,28)(19,26)(21,24)(22,25)(23,39)(27,31)(30,34)(32,42)(33,37)(35,38)(36,45)(40,41)(43,44);(14,16)(15,21,22,35)(17,29)(18,28)(19,26)(20,24,25,38)(23,40,37,36)(27,31)(30,34)(32,42)(33,45,39,41)(43,44);(16,26)(20,25)(21,35)(27,29)(28,42)(33,39)(34,43)(36,40)832 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 26416);