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×#60828 |
| 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 | |
2018 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)(24,32)(25,36)(26,28)(27,40)(29,35)(30,37)(31,39)(33,47)(34,45)(38,44)(41,42)(43,53)(46,48)(49,50)(51,52);(14,16,17,21)(15,18,19,20)(23,28)(29,42)(30,36)(31,40)(32,45)(43,50)(44,51)(46,47);(16,21)(18,20)(22,24,26,34)(23,29,28,42)(25,33,37,48)(27,41,39,35)(30,43,36,50)(31,45,40,32)(38,53,52,49)(44,47,51,46);(15,19)(18,20)(22,25)(23,30)(24,33)(26,37)(27,38)(28,36)(29,43)(31,44)(32,46)(34,48)(35,49)(39,52)(40,51)(41,53)(42,50)(45,47);(25,37)(30,36)(33,48)(38,52)(43,50)(44,51)(46,47)(49,53)598 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 53816);