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×#60819 |
| 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 | |
2058 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)(24,33)(25,37)(26,31)(27,29)(28,34)(30,38)(32,40)(35,42)(36,41)(39,45)(43,48)(44,50)(46,47)(49,52)(51,53);(14,16,17,21)(15,18,19,20)(22,24)(23,28)(25,35)(26,34)(27,36)(29,43)(30,42)(31,33)(32,41)(37,46)(38,47)(39,49)(40,48)(44,52)(45,51)(50,53);(16,21)(18,20)(23,29)(24,34)(27,40)(28,41)(30,44)(31,32)(33,43)(35,47)(37,45)(39,50)(42,51)(46,52);(15,19)(18,20)(22,25)(23,30)(24,35)(26,38)(27,39)(28,42)(29,44)(31,37)(32,45)(33,46)(34,47)(36,49)(40,50)(41,51)(43,52)(48,53);(25,38)(30,37)(35,47)(39,50)(42,46)(44,45)(49,53)(51,52)676 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 53807);