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×#33818 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C13 |
| prime radical | C13×#466 | C22 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C2×C42×C13 ◁ C2×C4×C8×C13 ◁ G | |
490 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)(22,23,27,32)(24,28,33,43)(25,29,38,46)(26,39,37,31)(30,47,45,36)(34,44,48,40)(35,52,49,42)(41,50,53,51);(14,15)(16,19)(17,18)(20,21)(22,24)(23,28)(25,34)(26,35)(27,33)(29,44)(30,41)(31,42)(32,43)(36,51)(37,49)(38,48)(39,52)(40,46)(45,53)(47,50);(15,18)(19,21)(23,29)(24,33)(25,36)(26,37)(28,40)(30,31)(32,46)(34,50)(38,47)(39,45)(41,52)(42,53)(43,44)(48,51);(14,16,17,20)(15,19,18,21)520 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 26806);