Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C13 · Schur multiplier (H2) = C28 |
| direct product | C13×#61925 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C13 |
| prime radical | C13×#3224 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C13×#533 ◁ G | |
1664 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)(16,24)(17,21)(18,22)(19,23)(20,26)(25,29)(27,28)(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);(14,16,19,26)(15,20,23,24)(17,25,18,27)(21,28,22,29)(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);(14,17,19,18)(15,21,23,22)(16,25,26,27)(20,28,24,29)(30,33,35,48)(31,38,40,53)(32,43,44,58)(34,47,36,50)(37,51,42,56)(39,46,41,55)(45,59,49,60)(52,57,54,61);(14,18,19,17)(15,22,23,21)(16,25,26,27)(20,28,24,29)(32,44)(37,42)(43,58)(45,49)(51,56)(52,54)(57,61)(59,60);(15,23)(20,24)(21,22)(28,29)(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, 54913);