Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33830 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C24 |
| direct product | C13×#33968 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C13 |
| prime radical | C13×#2250 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C4×Q8×C13 ◁ C8×Q8×C13 ◁ G | |
516 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)(15,19)(20,21)(22,23)(24,33)(25,30)(26,38)(27,42)(28,32)(29,36)(31,40)(34,49)(35,50)(37,48)(39,45)(41,52)(43,47)(44,51)(46,53);(14,15,18,19)(16,20,17,21)(24,34)(29,44)(33,49)(35,43)(36,51)(39,53)(45,46)(47,50);(14,16,18,17)(15,20,19,21)(22,24)(23,29)(25,35)(26,39)(27,43)(28,34)(30,45)(31,47)(32,44)(33,38)(36,40)(37,51)(41,53)(42,46)(48,50)(49,52);(14,17,18,16)(15,20,19,21)(22,25,28,27)(23,30,32,42)(24,35,34,43)(26,37,41,40)(29,45,44,46)(31,38,48,52)(33,50,49,47)(36,39,51,53)559 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 26956);