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×#61096 |
| 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×#532 ◁ G | |
2686 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)(18,19,23,27)(20,25,30,42)(21,26,34,44)(22,35,38,28)(24,36,40,31)(29,41,47,43)(32,49,48,39)(33,46,37,45);(18,20)(19,24)(21,32)(22,36)(23,30)(25,35)(26,43)(27,40)(28,42)(29,33)(31,38)(34,48)(37,47)(39,45)(41,44)(46,49);(15,17)(18,20)(19,25)(21,29)(22,31)(23,30)(24,35)(26,41)(27,42)(28,40)(32,33)(34,47)(36,38)(37,48)(39,45)(43,44)(46,49);(18,21,23,34)(19,26,27,44)(20,29,30,47)(22,37,38,33)(24,39,40,49)(25,41,42,43)(28,46,35,45)(31,48,36,32);(19,27)(20,30)(26,44)(28,35)(29,47)(31,36)(32,48)(45,46)715 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 54084);