Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #21776 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C13 · Schur multiplier (H2) = C26 |
| direct product | C13×#21780 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C13 | #2308 |
| commutator | C23 | C23×C4×C13 |
| Frattini, cosocle | C22×C4 | C24×C13 |
| prime radical | C13×#3486 | C2 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C13 ◁ C22×C4×C13 ◁ G | |
1236 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)(14,15,18,23,19,22,33,37)(16,24,27,38,26,20,31,35)(17,28,29,39,30,21,32,36)(25,34,42,44,41,40,43,45);(14,16)(15,20)(17,25)(18,31)(19,26)(21,34)(22,24)(23,38)(27,33)(28,40)(29,43)(30,41)(32,42)(35,37)(36,45)(39,44);(20,24)(34,40)(35,38)(44,45);(14,17,19,30)(15,21,22,28)(16,25,26,41)(18,32,33,29)(20,34,24,40)(23,39,37,36)(27,43,31,42)(35,45,38,44)598 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 14768);