Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #63041 |
| automorphism | ? |
| homology | Abelianization (H1) = C26×C13 · Schur multiplier (H2) = C213 |
| direct product | C13×#63063 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C26 |
| commutator, Frattini, cosocle | C22 | C26×C13 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ G | |
6916 conjugacy classes of subgroups.
| minimal degree | μ(G) = 53 |
| transitive degree | μt(G) = 832 |
A minimal faithful permutation representation — 6 generators on 53 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,18,19)(16,17,20,21)(22,23,28,32)(24,33,34,29)(25,30,38,44)(26,27,31,41)(35,46,48,42)(36,47,43,37)(39,40,45,51)(49,53,52,50);(15,19)(16,20)(24,34)(25,38)(29,33)(30,44)(36,43)(37,47)(39,45)(40,51);(14,16)(15,17)(18,20)(19,21)(22,24,28,34)(23,29,32,33)(25,35,38,48)(26,36,31,43)(27,37,41,47)(30,42,44,46)(39,49,45,52)(40,50,51,53);(14,17)(15,16)(18,21)(19,20)(22,25)(23,30)(24,35)(26,39)(27,40)(28,38)(29,42)(31,45)(32,44)(33,46)(34,48)(36,49)(37,50)(41,51)(43,52)(47,53);(22,26)(23,27)(24,36)(25,39)(28,31)(29,37)(30,40)(32,41)(33,47)(34,43)(35,49)(38,45)(42,50)(44,51)(46,53)(48,52);(22,27)(23,31)(24,37)(25,40)(26,32)(28,41)(29,43)(30,45)(33,36)(34,47)(35,50)(38,51)(39,44)(42,52)(46,49)(48,53)910 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 56051);