Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #61049 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C13 · Schur multiplier (H2) = C29 |
| direct product | C13×#61054 |
| 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 | |
2710 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)(20,29)(21,26)(22,27)(23,36)(24,28)(25,30)(31,46)(32,39)(33,42)(34,49)(35,44)(37,41)(38,45)(40,47)(43,48);(18,20,24,32)(19,25,28,41)(21,30,23,37)(22,34,35,47)(26,39,36,29)(27,43,44,46)(31,38,48,33)(40,42,49,45);(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)(25,41)(26,36)(27,44)(29,39)(40,49)(42,45)(43,46)754 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 54042);