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×#33426 |
| 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 | C2×C13×#41 | C2×C4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C13 ◁ C2×C13×#97 ◁ G | |
520 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)(14,15,17,23,18,24,31,40,19,22,30,38,32,21,36,37)(16,25,27,39,28,33,42,44,26,20,29,34,41,35,43,45);(14,16)(15,20)(17,29)(18,28)(19,26)(21,33)(22,25)(23,39)(24,35)(27,30)(31,43)(32,41)(34,38)(36,42)(37,45)(40,44);(15,21,22,24)(17,30)(20,33,25,35)(23,40,38,37)(27,29)(31,36)(34,45,39,44)(42,43);(16,26)(20,25)(27,29)(28,41)(33,35)(34,39)(42,43)(44,45)754 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 26414);