Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23886 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C24 |
| direct product | C13×#25985 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | D42 |
| commutator, Frattini, cosocle | C22×C4 | C24×C13 |
| prime radical | C2×C13×2−1+4 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C22×C4×C13 ◁ G | |
842 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)(14,15,17,19)(16,20,21,18)(22,23)(24,34)(25,29)(26,32)(27,33)(28,37)(30,39)(31,43)(35,48)(36,45)(38,46)(40,49)(41,50)(42,47)(44,51)(52,53);(22,24,27,38)(23,28,33,47)(25,36,41,51)(26,42,43,37)(29,48,50,53)(30,45,49,44)(31,46,32,34)(35,39,52,40);(14,16,17,21)(15,18,19,20)(22,25)(23,29)(24,35)(26,39)(27,41)(28,44)(30,32)(31,49)(33,50)(34,48)(36,42)(37,51)(38,52)(40,43)(45,47)(46,53);(22,25)(23,30)(24,36)(26,40)(27,41)(28,45)(29,32)(31,50)(33,49)(34,48)(35,42)(37,52)(38,51)(39,43)(44,47)(46,53)559 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 18973);