Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33522 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C24 |
| direct product | C13×#33686 |
| 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 | |
544 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)(23,28)(24,32)(26,37)(27,36)(29,43)(30,46)(33,51)(34,52)(35,50)(38,39)(40,44)(41,48)(45,47)(49,53);(15,18)(19,21)(22,23)(24,29)(25,28)(26,30)(27,31)(32,44)(33,40)(34,45)(35,41)(36,42)(37,48)(38,47)(39,49)(43,51)(46,50)(52,53);(22,24,25,33)(23,29,28,40)(26,38,35,52)(27,39,36,34)(30,47,41,53)(31,49,42,45)(32,50,51,37)(43,48,44,46);(14,16,17,20)(15,19,18,21)(23,28)(29,40)(30,41)(31,42)(43,44)(45,49)(46,48)(47,53)598 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 26674);