Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #9369 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C13 · Schur multiplier (H2) = C23 |
| direct product | C13×#9374 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | #386 |
| commutator | C42 | C22×C4×C13 |
| Frattini, cosocle | C2×C42 | C23×C13 |
| prime radical | C23×C13 | #123 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C2×C42×C13 ◁ G | |
368 conjugacy classes of subgroups.
| minimal degree | μ(G) = 61 |
| transitive degree | μt(G) = 1664 |
A minimal faithful permutation representation — 3 generators on 61 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,20,23,18,17,19,22)(16,24,26,28,27,21,25,29)(30,31,35,39,36,40,34,50)(32,41,45,52,44,56,43,37)(33,46,48,54,49,38,47,53)(42,55,59,51,58,61,57,60);(14,16,20,25,18,27,19,26)(15,21,22,29,17,24,23,28)(30,32,36,44)(31,37)(33,42,49,58)(34,43,35,45)(38,51)(39,41)(40,52)(46,60)(47,57,48,59)(50,56)(53,61)(54,55);(14,17,18,15)(16,24,27,21)(19,22,20,23)(25,28,26,29)(30,33,36,49)(31,38,40,46)(32,42,44,58)(34,48,35,47)(37,51,52,60)(39,54,50,53)(41,55,56,61)(43,59,45,57)481 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 2362);