Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #60753 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C13 · Schur multiplier (H2) = C28 |
| direct product | C13×#60869 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C13 |
| prime radical | C24×C13 | C2×D4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C2×C13×#117 ◁ G | |
1626 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)(17,20)(18,21)(19,24)(23,28)(25,27)(26,29)(30,31,36,41)(32,37,43,51)(33,46,48,55)(34,40,35,39)(38,49,54,47)(42,56,57,61)(44,53,45,52)(50,59,60,58);(14,16,18,24)(15,19,21,22)(17,25,26,23)(20,28,29,27)(30,32)(31,37)(33,42)(34,44)(35,45)(36,43)(38,50)(39,52)(40,53)(41,51)(46,56)(47,58)(48,57)(49,59)(54,60)(55,61);(14,17,18,26)(15,20,21,29)(16,23,24,25)(19,27,22,28)(30,33)(31,38)(32,42)(34,47)(35,49)(36,48)(37,50)(39,46)(40,55)(41,54)(43,57)(44,58)(45,59)(51,60)(52,56)(53,61);(15,21)(19,22)(20,29)(27,28)(32,43)(37,51)(42,57)(44,45)(50,60)(52,53)(56,61)(58,59);(30,34,36,35)(31,39,41,40)(32,44,43,45)(33,47,48,49)(37,52,51,53)(38,46,54,55)(42,58,57,59)(50,56,60,61)598 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 53857);