Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C13 · Schur multiplier (H2) = C28 |
| direct product | C13×#61642 |
| 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 | |
2042 conjugacy classes of subgroups.
| minimal degree | μ(G) = 53 |
| transitive degree | μt(G) = 832 |
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)(22,23,28,32)(24,29,34,43)(25,36,38,46)(26,31,27,40)(30,41,47,37)(33,48,49,53)(35,44,39,45)(42,50,52,51);(14,16)(15,18)(17,21)(19,20)(22,24,28,34)(23,29,32,43)(25,33,38,49)(26,39,27,35)(30,42,47,52)(31,45,40,44)(36,48,46,53)(37,51,41,50);(22,25)(23,30)(24,33)(26,37)(27,41)(28,38)(29,42)(31,46)(32,47)(34,49)(35,50)(36,40)(39,51)(43,52)(44,48)(45,53);(16,21)(18,20)(24,34)(29,43)(33,49)(35,39)(42,52)(44,45)(48,53)(50,51);(15,19)(18,20)(22,26,28,27)(23,31,32,40)(24,35,34,39)(25,37,38,41)(29,44,43,45)(30,46,47,36)(33,50,49,51)(42,48,52,53)676 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 54630);