Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #61071 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C13 · Schur multiplier (H2) = C29 |
| direct product | C13×#61078 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C13 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C13×#525 ◁ G | |
2694 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 832 |
A minimal faithful permutation representation — 5 generators on 49 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15)(16,17)(18,19,24,28)(20,29,32,39)(21,26,23,36)(22,27,35,44)(25,37,41,30)(31,46,48,43)(33,42,38,45)(34,49,47,40);(18,20)(19,25)(21,30)(22,34)(23,37)(24,32)(26,39)(27,43)(28,41)(29,36)(31,33)(35,47)(38,48)(40,45)(42,49)(44,46);(15,17)(18,21,24,23)(19,26,28,36)(20,30,32,37)(22,33,35,38)(25,39,41,29)(27,42,44,45)(31,47,48,34)(40,43,49,46);(18,22,24,35)(19,27,28,44)(20,31,32,48)(21,33,23,38)(25,40,41,49)(26,42,36,45)(29,46,39,43)(30,47,37,34);(19,28)(20,32)(26,36)(27,44)(30,37)(31,48)(34,47)(42,45)715 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 54066);