Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C13 · Schur multiplier (H2) = C24 |
| direct product | C13×#17991 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C13 | C22×D4 |
| commutator | C2×C4 | C23×C4×C13 |
| Frattini, cosocle | C42 | C24×C13 |
| socle | C22×C13 | C2×C4×D4 |
| prime radical | C23×C13 | C4×D4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C13 ◁ C13×#431 ◁ G | |
544 conjugacy classes of subgroups.
| minimal degree | μ(G) = 61 |
| transitive degree | μt(G) = 1664 |
A minimal faithful permutation representation — 4 generators on 61 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,18,22,19,21,27,28)(16,20,24,17,23,25,29,26)(30,31)(32,40)(33,37)(34,46)(35,38)(36,42)(39,48)(41,54)(43,53)(44,52)(45,58)(47,50)(49,56)(51,57)(55,61)(59,60);(14,16)(15,20)(17,22)(18,24)(19,23)(21,25)(26,28)(27,29)(30,32,35,43)(31,36,38,50)(33,41,44,55)(34,47,48,42)(37,49,52,60)(39,53,46,40)(45,59,57,56)(51,61,58,54);(14,17,18,25,19,26,27,20)(15,16,22,24,21,23,28,29)(30,33,35,44)(31,37,38,52)(32,41,43,55)(34,45,48,57)(36,49,50,60)(39,51,46,58)(40,54,53,61)(42,56,47,59);(15,21)(16,23)(22,28)(24,29)(31,38)(33,44)(36,50)(39,46)(40,53)(41,55)(45,57)(56,59)676 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 10979);