Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #24398 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C23×C4 |
| direct product | C13×#24525 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C2×#121 |
| commutator, Frattini, cosocle | C22×C4 | C24×C13 |
| prime radical | C22×C13×#41 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C23×C4×C13 ◁ G | |
858 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)(16,20)(17,19)(18,21)(22,23,26,31,28,33,27,32)(24,29,35,44,37,46,36,45)(25,38,42,30,41,49,40,48)(34,50,39,43,52,47,51,53);(14,16,17,21)(15,18,19,20)(22,24)(23,29)(25,39)(26,35)(27,36)(28,37)(30,47)(31,44)(32,45)(33,46)(34,40)(38,43)(41,51)(42,52)(48,50)(49,53);(22,25)(23,30)(24,34)(26,40)(27,42)(28,41)(29,43)(31,38)(32,49)(33,48)(35,51)(36,39)(37,52)(44,50)(45,47)(46,53);(15,19)(18,20)(22,26,28,27)(23,31,33,32)(24,35,37,36)(25,40,41,42)(29,44,46,45)(30,38,48,49)(34,51,52,39)(43,50,53,47)559 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 17513);