Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C13 · Schur multiplier (H2) = C28 |
| direct product | C13×#61418 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C13 |
| prime radical | C13×#3154 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C13×#533 ◁ G | |
1854 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)(15,19)(20,21)(22,23)(24,29)(25,36)(26,32)(27,40)(28,31)(30,37)(33,48)(34,44)(35,43)(38,47)(39,45)(41,46)(42,50)(49,52)(51,53);(14,15,18,19)(16,20,17,21)(22,24,28,35)(23,29,31,43)(25,33,38,51)(26,39,27,34)(30,42,46,52)(32,45,40,44)(36,48,47,53)(37,50,41,49);(14,16,18,17)(15,20,19,21)(22,25)(23,30)(24,33)(26,37)(27,41)(28,38)(29,42)(31,46)(32,47)(34,49)(35,51)(36,40)(39,50)(43,52)(44,48)(45,53);(14,17,18,16)(15,20,19,21)(23,31)(29,43)(30,46)(32,40)(36,47)(42,52)(44,45)(48,53);(22,26,28,27)(23,32,31,40)(24,34,35,39)(25,37,38,41)(29,44,43,45)(30,47,46,36)(33,49,51,50)(42,48,52,53)676 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 54406);