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×#33884 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C13 |
| prime radical | C13×#3287 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C4×D4×C13 ◁ C8×D4×C13 ◁ G | |
552 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)(14,15,17,19)(16,20,21,18)(22,23,28,32)(24,33,34,50)(25,30,27,42)(26,38,41,51)(29,44,45,36)(31,37,49,40)(35,52,43,48)(39,46,53,47);(14,16)(15,18)(17,21)(19,20)(24,34)(29,45)(33,50)(35,43)(36,44)(39,53)(46,47)(48,52);(22,24,28,34)(23,29,32,45)(25,35,27,43)(26,39,41,53)(30,46,42,47)(31,48,49,52)(33,51,50,38)(36,37,44,40);(16,21)(18,20)(22,25,28,27)(23,30,32,42)(24,35,34,43)(26,37,41,40)(29,46,45,47)(31,38,49,51)(33,52,50,48)(36,39,44,53)559 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 26872);