Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #60457 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C13 · Schur multiplier (H2) = C27×C4 |
| direct product | C13×#60624 |
| 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 ◁ C4×C13×#41 ◁ G | |
2038 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)(24,34)(25,29)(26,31)(27,42)(28,33)(30,37)(32,35)(36,48)(38,43)(39,44)(40,46)(41,52)(45,50)(47,49)(51,53);(15,18)(19,21)(22,24,35,39,28,37,27,25)(23,29,42,30,33,44,32,34)(26,36,49,51,40,50,41,38)(31,43,52,45,46,53,47,48);(14,16,17,20)(15,19,18,21)(22,25,27,37,28,39,35,24)(23,30,32,29,33,34,42,44)(26,38,41,50,40,51,49,36)(31,45,47,43,46,48,52,53);(22,26)(23,31)(24,36)(25,38)(27,41)(28,40)(29,43)(30,45)(32,47)(33,46)(34,48)(35,49)(37,50)(39,51)(42,52)(44,53);(26,40)(31,46)(36,50)(38,51)(41,49)(43,53)(45,48)(47,52)832 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 53612);