Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33522 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C25 |
| direct product | C13×#33590 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C13 |
| prime radical | C2×C13×#508 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C13×#117 ◁ C13×#405 ◁ G | |
694 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 1664 |
A minimal faithful permutation representation — 4 generators on 49 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(15,17)(18,19,24,29)(20,25,32,43)(21,27,23,39)(22,35,38,49)(26,44,46,31)(28,34,47,37)(30,40,33,42)(36,41,48,45);(14,15,16,17)(18,20)(19,25)(21,33)(22,31)(23,30)(24,32)(26,35)(27,42)(28,41)(29,43)(34,48)(36,37)(38,44)(39,40)(45,47)(46,49);(18,20)(19,26)(21,30)(22,36)(23,33)(24,32)(25,35)(27,41)(28,42)(29,46)(31,37)(34,44)(38,48)(39,45)(40,47)(43,49);(18,21,24,23)(19,27,29,39)(20,30,32,33)(22,34,38,37)(25,40,43,42)(26,41,46,45)(28,35,47,49)(31,36,44,48)598 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 26578);