Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C13 · Schur multiplier (H2) = C28 |
| direct product | C13×#60859 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C13 | C22×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C13 |
| socle | C22×C13 | C23×D4 |
| prime radical | C13×#3455 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C13 ◁ C2×C13×#117 ◁ 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)(32,37)(33,45)(34,39)(35,48)(36,40)(38,46)(41,55)(42,51)(43,52)(44,58)(47,53)(49,54)(50,57)(56,61)(59,60);(14,16,18,24)(15,19,21,22)(17,25,26,23)(20,28,29,27)(30,32)(31,37)(33,41)(34,43)(35,44)(36,42)(38,50)(39,52)(40,51)(45,55)(46,57)(47,56)(48,58)(49,59)(53,61)(54,60);(14,17,18,26)(15,20,21,29)(16,23,24,25)(19,27,22,28)(30,33)(31,38)(32,41)(34,46)(35,49)(36,47)(37,50)(39,53)(40,54)(42,56)(43,57)(44,59)(45,48)(51,60)(52,61)(55,58);(15,21)(19,22)(20,29)(27,28)(32,42)(37,51)(41,56)(43,44)(50,60)(52,58)(55,61)(57,59);(30,34,36,35)(31,39,40,48)(32,43,42,44)(33,46,47,49)(37,52,51,58)(38,53,54,45)(41,57,56,59)(50,61,60,55)676 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 53847);