Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C13 · Schur multiplier (H2) = C28 |
| direct product | C13×#62571 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C13 |
| prime radical | C13×#3561 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C13×#529 ◁ G | |
1656 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)(16,23)(17,21)(18,27)(19,22)(20,25)(24,29)(26,28)(30,31,34,38)(32,40,42,36)(33,44,45,60)(35,48,47,39)(37,51,52,46)(41,55,56,59)(43,50,58,54)(49,57,53,61);(14,16)(15,20)(17,24)(18,26)(19,25)(21,28)(22,23)(27,29)(30,32)(31,36)(33,41)(34,42)(35,43)(37,49)(38,40)(39,50)(44,59)(45,56)(46,57)(47,58)(48,54)(51,61)(52,53)(55,60);(14,17,19,18)(15,21,22,27)(16,24,25,26)(20,28,23,29)(30,33,35,46,34,45,47,51)(31,37,39,44,38,52,48,60)(32,41,43,57,42,56,58,61)(36,49,50,59,40,53,54,55);(16,25)(20,23)(24,26)(28,29)(32,42)(33,45)(36,40)(37,52)(43,58)(44,60)(46,51)(50,54);(14,18,19,17)(15,21,22,27)(16,26,25,24)(20,28,23,29)(31,38)(32,42)(37,52)(39,48)(41,56)(43,58)(44,60)(57,61)598 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 55559);