Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #62862 |
| automorphism | ? |
| homology | Abelianization (H1) = C26×C13 · Schur multiplier (H2) = C213 |
| direct product | C13×#62873 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C26 |
| commutator, Frattini, cosocle | C22 | C26×C13 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ G | |
6282 conjugacy classes of subgroups.
| minimal degree | μ(G) = 61 |
| transitive degree | μt(G) = 832 |
A minimal faithful permutation representation — 6 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)(31,36)(34,46)(37,40)(38,47)(42,56)(45,57)(49,52)(55,61);(14,15,18,21)(16,19,24,22)(17,20,25,27)(23,26,29,28)(33,44)(38,47)(41,54)(45,57)(49,52)(51,58)(55,61)(59,60);(14,15)(16,19)(17,20)(18,21)(22,24)(23,26)(25,27)(28,29)(30,31,35,36)(32,40,43,37)(33,38,44,47)(34,39,46,48)(41,52,54,49)(42,53,56,50)(45,51,57,58)(55,60,61,59);(14,16)(15,19)(17,23)(18,24)(20,26)(21,22)(25,29)(27,28)(30,32,35,43)(31,37,36,40)(33,41,44,54)(34,42,46,56)(38,49,47,52)(39,50,48,53)(45,55,57,61)(51,59,58,60);(14,17,18,25)(15,20,21,27)(16,23,24,29)(19,26,22,28)(30,33)(31,38)(32,41)(34,45)(35,44)(36,47)(37,49)(39,51)(40,52)(42,55)(43,54)(46,57)(48,58)(50,59)(53,60)(56,61);(30,34)(31,39)(32,42)(33,45)(35,46)(36,48)(37,50)(38,51)(40,53)(41,55)(43,56)(44,57)(47,58)(49,59)(52,60)(54,61)910 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 55861);