Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #60771 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C13 · Schur multiplier (H2) = C28 |
| direct product | C13×#61005 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C13 |
| prime radical | C13×#3197 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C2×C13×#117 ◁ G | |
1672 conjugacy classes of subgroups.
| minimal degree | μ(G) = 61 |
| transitive degree | μt(G) = 832 |
A minimal faithful permutation representation — 5 generators on 61 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15)(16,22)(17,21)(18,20)(19,23)(24,28)(25,27)(26,29)(30,31,35,39)(32,40,41,53)(33,37,44,51)(34,46,48,38)(36,47,49,43)(42,54,55,61)(45,58,57,52)(50,59,60,56);(14,16)(15,19)(17,24)(18,23)(20,22)(21,26)(25,29)(27,28)(32,41)(36,49)(40,53)(42,55)(43,47)(50,60)(54,61)(56,59);(16,23)(19,22)(24,29)(26,28)(30,32,35,41)(31,36,39,49)(33,42,44,55)(34,47,48,43)(37,50,51,60)(38,53,46,40)(45,59,57,56)(52,61,58,54);(15,20)(19,22)(21,27)(26,28)(30,33)(31,37)(32,42)(34,45)(35,44)(36,50)(38,52)(39,51)(40,54)(41,55)(43,56)(46,58)(47,59)(48,57)(49,60)(53,61);(14,17,18,25)(15,21,20,27)(16,24,23,29)(19,26,22,28)(33,44)(37,51)(42,55)(45,57)(50,60)(52,58)(54,61)(56,59)598 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 53993);