Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C13 · Schur multiplier (H2) = C28 |
| direct product | C13×#61691 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C13 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C13×#532 ◁ G | |
2046 conjugacy classes of subgroups.
| minimal degree | μ(G) = 53 |
| transitive degree | μt(G) = 832 |
A minimal faithful permutation representation — 5 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)(22,23,27,33)(24,35,38,29)(25,31,40,47)(26,34,28,32)(30,42,46,39)(36,50,52,44)(37,45,41,48)(43,53,49,51);(14,16)(15,18)(17,21)(19,20)(22,24,27,38)(23,29,33,35)(25,36,40,52)(26,41,28,37)(30,43,46,49)(31,44,47,50)(32,48,34,45)(39,53,42,51);(22,25)(23,30)(24,36)(26,39)(27,40)(28,42)(29,43)(31,32)(33,46)(34,47)(35,49)(37,51)(38,52)(41,53)(44,48)(45,50);(16,21)(18,20)(22,25)(23,31)(24,36)(26,42)(27,40)(28,39)(29,44)(30,32)(33,47)(34,46)(35,50)(37,53)(38,52)(41,51)(43,48)(45,49);(15,19)(18,20)(22,26,27,28)(23,32,33,34)(24,37,38,41)(25,39,40,42)(29,45,35,48)(30,31,46,47)(36,51,52,53)(43,50,49,44)637 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 54679);