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×#61076 |
| 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 | |
2672 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)(18,19,23,26)(20,28,30,44)(21,25,34,42)(22,35,38,27)(24,36,40,31)(29,46,47,41)(32,49,48,39)(33,45,37,43);(18,20)(19,24)(21,32)(22,36)(23,30)(25,41)(26,40)(27,44)(28,35)(29,33)(31,38)(34,48)(37,47)(39,43)(42,46)(45,49);(15,17);(18,21,23,34)(19,25,26,42)(20,29,30,47)(22,37,38,33)(24,39,40,49)(27,45,35,43)(28,46,44,41)(31,48,36,32);(19,26)(20,30)(25,42)(27,35)(29,47)(31,36)(32,48)(43,45)715 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 54064);