Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23912 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C25 |
| direct product | C13×#24183 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C13 |
| prime radical | C13×#532 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C2×C42×C13 ◁ G | |
1002 conjugacy classes of subgroups.
| minimal degree | μ(G) = 53 |
| transitive degree | μt(G) = 832 |
A minimal faithful permutation representation — 4 generators on 53 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15)(16,20)(17,18)(19,21)(22,23)(24,28)(25,35)(26,38)(27,31)(29,37)(30,41)(32,49)(33,47)(34,44)(36,48)(39,43)(40,46)(42,51)(45,52)(50,53);(15,18)(19,20)(22,24,27,34)(23,28,31,44)(25,32,36,50)(26,39,41,33)(29,45,46,42)(30,47,38,43)(35,49,48,53)(37,52,40,51);(22,25,27,36)(23,29,31,46)(24,32,34,50)(26,40,41,37)(28,42,44,45)(30,48,38,35)(33,52,39,51)(43,53,47,49);(14,16,17,21)(15,19,18,20)(25,36)(29,46)(32,50)(35,48)(37,40)(42,45)(49,53)(51,52)520 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 17171);