Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C13 · Schur multiplier (H2) = C28 |
| direct product | C13×#60685 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C13 | C22×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C13 |
| socle | C22×C13 | C23×D4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C13 ◁ C2×C13×#117 ◁ G | |
1878 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)(16,19)(17,18)(20,21)(22,23)(24,29)(25,37)(26,31)(27,42)(28,32)(30,40)(33,48)(34,44)(35,45)(36,51)(38,52)(39,47)(41,53)(43,50)(46,49);(15,18)(19,21)(22,24)(23,29)(25,38)(26,35)(27,36)(28,34)(30,46)(31,45)(32,44)(33,41)(37,52)(39,50)(40,49)(42,51)(43,47)(48,53);(22,25,27,40,28,41,26,39)(23,30,31,37,32,47,42,53)(24,33,36,50,34,38,35,49)(29,43,45,48,44,46,51,52);(14,16,17,20)(15,19,18,21)(24,34)(29,44)(33,38)(35,36)(43,46)(45,51)(48,52)(49,50);(22,26,28,27)(23,31,32,42)(24,35,34,36)(25,39,41,40)(29,45,44,51)(30,37,47,53)(33,49,38,50)(43,48,46,52)832 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 53673);