Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #60768 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C13 · Schur multiplier (H2) = C27×C4 |
| direct product | C13×#60823 |
| 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 | |
2054 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)(24,34)(25,40)(26,32)(27,33)(28,44)(29,38)(30,41)(31,42)(35,50)(36,46)(37,51)(39,47)(43,49)(45,53)(48,52);(14,16,17,21)(15,18,19,20)(22,24)(23,29)(25,36)(26,37)(27,38)(28,39)(30,48)(31,46)(32,47)(33,34)(35,42)(40,50)(41,53)(43,52)(44,51)(45,49);(16,21)(18,20)(22,25)(23,30)(24,35)(26,41)(27,42)(28,43)(29,45)(31,32)(33,49)(34,48)(36,38)(37,52)(39,53)(40,44)(46,51)(47,50);(15,19)(18,20)(22,25)(23,31)(24,36)(26,43)(27,42)(28,41)(29,46)(30,32)(33,40)(34,50)(35,38)(37,52)(39,53)(44,49)(45,51)(47,48);(22,26,27,28)(23,32,33,44)(24,37,38,39)(25,41,42,43)(29,47,34,51)(30,31,49,40)(35,52,36,53)(45,50,48,46)676 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 53811);