Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C13 · Schur multiplier (H2) = C28 |
| direct product | C13×#61862 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C13 |
| prime radical | C13×#449 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C13×#533 ◁ G | |
1614 conjugacy classes of subgroups.
| minimal degree | μ(G) = 61 |
| transitive degree | μt(G) = 1664 |
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)(30,31,35,40)(32,42,44,37)(33,46,48,55)(34,41,36,39)(38,50,53,47)(43,57,58,61)(45,52,49,54)(51,60,56,59);(14,16,18,24)(15,19,21,22)(17,25,26,23)(20,28,29,27)(30,32,35,44)(31,37,40,42)(33,43,48,58)(34,49,36,45)(38,51,53,56)(39,54,41,52)(46,61,55,57)(47,60,50,59);(30,33)(31,38)(32,43)(34,47)(35,48)(36,50)(37,51)(39,46)(40,53)(41,55)(42,56)(44,58)(45,59)(49,60)(52,57)(54,61);(14,17,18,26)(15,20,21,29)(16,23,24,25)(19,27,22,28)(32,44)(37,42)(43,58)(45,49)(51,56)(52,54)(57,61)(59,60);(15,21)(19,22)(20,29)(27,28)(30,34,35,36)(31,39,40,41)(32,45,44,49)(33,47,48,50)(37,52,42,54)(38,46,53,55)(43,59,58,60)(51,57,56,61)637 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 54850);