Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #60756 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C13 · Schur multiplier (H2) = C28 |
| direct product | C13×#60927 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C13 |
| prime radical | C13×#3062 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C4×C13×#41 ◁ G | |
1772 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)(15,18)(16,20)(22,23)(24,32)(25,36)(26,30)(27,41)(28,34)(29,39)(31,40)(33,49)(35,44)(37,53)(38,47)(42,46)(43,52)(45,50)(48,51);(14,15)(16,19)(17,18)(20,21)(22,24)(23,28)(25,37)(26,34)(27,35)(29,45)(30,32)(31,44)(33,38)(36,49)(39,52)(40,51)(41,48)(42,50)(43,46)(47,53);(15,18)(19,21)(22,25,26,38)(23,29,30,46)(24,33,34,37)(27,42,40,39)(28,43,32,45)(31,47,41,36)(35,52,51,50)(44,49,48,53);(14,16,17,20)(15,19,18,21)(23,30)(28,32)(29,46)(31,41)(36,47)(43,45)(44,48)(49,53);(24,34)(28,32)(33,37)(35,51)(43,45)(44,48)(49,53)(50,52)637 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 53915);