Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #60768 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C13 · Schur multiplier (H2) = C28 |
| direct product | C13×#60879 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C13 |
| prime radical | C13×#535 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C4×C13×#41 ◁ G | |
1654 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)(32,36)(33,38)(34,37)(35,40)(39,46)(41,48)(42,47)(43,50)(44,52)(45,51)(49,56)(53,57)(54,59)(55,58)(60,61);(14,16,18,24)(15,19,21,22)(17,25,26,23)(20,28,29,27)(30,32,35,43)(31,36,40,50)(33,41,44,54)(34,42,46,56)(37,47,39,49)(38,48,52,59)(45,55,57,61)(51,58,53,60);(14,17,18,26)(15,20,21,29)(16,23,24,25)(19,27,22,28)(31,37)(34,46)(36,47)(38,51)(39,40)(42,56)(45,57)(48,58)(49,50)(52,53)(55,61)(59,60);(15,21)(19,22)(20,29)(27,28)(30,33)(31,38)(32,41)(34,45)(35,44)(36,48)(37,51)(39,53)(40,52)(42,55)(43,54)(46,57)(47,58)(49,60)(50,59)(56,61);(33,44)(38,52)(41,54)(45,57)(48,59)(51,53)(55,61)(58,60)676 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 53867);