Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C13 · Schur multiplier (H2) = C28 |
| direct product | C13×#61674 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C13 |
| prime radical | C13×#3500 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C13×#532 ◁ G | |
2032 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)(22,23,28,33)(24,29,37,47)(25,31,39,49)(26,32,27,42)(30,41,50,38)(34,51,35,44)(36,45,40,46)(43,52,48,53);(14,16)(15,18)(17,21)(19,20)(22,24)(23,29)(25,35)(26,40)(27,36)(28,37)(30,48)(31,44)(32,46)(33,47)(34,39)(38,52)(41,53)(42,45)(43,50)(49,51);(22,25)(23,30)(24,34)(26,38)(27,41)(28,39)(29,43)(31,42)(32,49)(33,50)(35,37)(36,52)(40,53)(44,46)(45,51)(47,48);(16,21)(18,20)(22,25)(23,31)(24,35)(26,41)(27,38)(28,39)(29,44)(30,42)(32,50)(33,49)(34,37)(36,52)(40,53)(43,46)(45,48)(47,51);(15,19)(18,20)(22,26,28,27)(23,32,33,42)(24,36,37,40)(25,38,39,41)(29,45,47,46)(30,49,50,31)(34,52,35,53)(43,51,48,44)598 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 54662);