Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #20671 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C13 · Schur multiplier (H2) = C24 |
| direct product | C13×#33427 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C13 | C2×#117 |
| commutator | C2×C4 | C23×C4×C13 |
| Frattini, cosocle | C2×C8 | C24×C13 |
| socle | C2×C13 | C2×#432 |
| prime radical | C24×C13 | M16 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C13 ◁ C13×#405 ◁ G | |
524 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)(14,15,17,22,18,23,30,38,19,20,28,33,31,34,43,45)(16,24,26,40,27,32,42,37,25,39,29,44,41,21,35,36);(15,20)(17,28)(21,32)(23,34)(24,39)(26,29)(30,43)(35,42);(14,16)(15,21,20,32)(17,29)(18,27)(19,25)(22,37,33,36)(23,24,34,39)(26,28)(30,35)(31,41)(38,44,45,40)(42,43);(16,25)(21,32)(24,39)(26,29)(27,41)(35,42)(36,37)(40,44)754 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 26415);