Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33607 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C24 |
| direct product | C13×#33743 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C13 |
| prime radical | C13×#3176 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C13×#117 ◁ C13×#405 ◁ G | |
508 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)(16,19)(17,18)(20,21)(24,32)(25,36)(26,37)(28,39)(30,45)(31,44)(33,38)(34,49)(35,48)(40,43)(41,50)(42,53)(46,47)(51,52);(15,18)(19,21)(22,23,27,29)(24,28,35,41)(25,30,38,43)(26,31,37,44)(32,39,48,50)(33,40,36,45)(34,42,46,51)(47,52,49,53);(22,24,33,49,26,34,25,32,27,35,36,47,37,46,38,48)(23,28,40,53,31,42,30,39,29,41,45,52,44,51,43,50);(14,16,17,20)(15,19,18,21)(23,29)(28,41)(30,43)(31,44)(39,50)(40,45)(42,51)(52,53)676 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 26731);