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×#21781 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C13 | #2308 |
| commutator | C23 | C23×C4×C13 |
| Frattini, cosocle | C22×C4 | C24×C13 |
| prime radical | C13×#3487 | C2 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C13 ◁ C22×C4×C13 ◁ G | |
1258 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)(14,15,19,25,20,24,17,22)(16,26,27,35,29,21,33,37)(18,31,30,39,32,23,34,38)(28,36,43,44,42,40,41,45);(14,16)(15,21)(17,27)(18,28)(19,33)(20,29)(22,37)(23,36)(24,26)(25,35)(30,41)(31,40)(32,42)(34,43)(38,45)(39,44);(14,17,20,19)(15,22,24,25)(16,27,29,33)(18,30,32,34)(21,35,26,37)(23,38,31,39)(28,41,42,43)(36,44,40,45);(14,18,20,32)(15,23,24,31)(16,28,29,42)(17,30,19,34)(21,36,26,40)(22,38,25,39)(27,41,33,43)(35,44,37,45)598 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 14769);