Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33758 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C24 |
| direct product | C13×#33822 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C13 |
| prime radical | C13×#2218 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C2×C42×C13 ◁ C2×C4×C8×C13 ◁ G | |
496 conjugacy classes of subgroups.
| minimal degree | μ(G) = 53 |
| transitive degree | μt(G) = 1664 |
A minimal faithful permutation representation — 4 generators on 53 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(15,18)(16,20)(22,23)(24,33)(25,30)(26,29)(27,40)(28,34)(31,39)(32,38)(35,46)(36,43)(37,44)(41,49)(42,53)(45,52)(47,51)(48,50);(14,15)(16,19)(17,18)(20,21)(22,24,25,34)(23,28,30,33)(26,35,37,49)(27,36,38,50)(29,41,44,46)(31,42,45,47)(32,43,40,48)(39,51,52,53);(15,18)(19,21)(23,29)(26,39)(27,38)(28,41)(30,44)(31,32)(33,46)(35,51)(36,50)(37,52)(40,45)(42,43)(47,48)(49,53);(14,16,17,20)(15,19,18,21)(23,30)(28,33)(29,44)(31,45)(32,40)(41,46)(42,47)(43,48)520 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 26810);