Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #60771 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C13 · Schur multiplier (H2) = C27×C4 |
| direct product | C13×#60831 |
| 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 ◁ C4×C13×#41 ◁ G | |
2014 conjugacy classes of subgroups.
| minimal degree | μ(G) = 53 |
| transitive degree | μt(G) = 1664 |
A minimal faithful permutation representation — 5 generators on 53 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15)(16,20)(17,19)(18,21)(22,23)(24,33)(25,37)(26,32)(27,29)(28,41)(30,35)(31,39)(34,49)(36,45)(38,47)(40,46)(42,43)(44,50)(48,51)(52,53);(14,16,17,21)(15,18,19,20)(23,29)(30,43)(31,37)(32,41)(33,45)(44,53)(46,47)(48,49);(16,21)(18,20)(22,24,27,36)(23,30,29,43)(25,34,39,51)(26,35,28,42)(31,44,37,53)(32,45,41,33)(38,50,40,52)(46,48,47,49);(15,19)(18,20)(22,25)(23,31)(24,34)(26,40)(27,39)(28,38)(29,37)(30,44)(32,47)(33,48)(35,52)(36,51)(41,46)(42,50)(43,53)(45,49);(22,26,27,28)(23,32,29,41)(24,35,36,42)(25,38,39,40)(30,45,43,33)(31,46,37,47)(34,50,51,52)(44,48,53,49)598 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 53819);