Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #62842 |
| automorphism | ? |
| homology | Abelianization (H1) = C26×C13 · Schur multiplier (H2) = C213 |
| direct product | C13×#62850 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C26 |
| commutator, Frattini, cosocle | C22 | C26×C13 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ G | |
6846 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)(15,18)(19,21)(23,28)(26,38)(29,32)(30,39)(34,48)(37,49)(41,44)(47,53);(14,15)(16,19)(17,18)(20,21)(25,36)(30,39)(33,46)(37,49)(41,44)(43,50)(47,53)(51,52);(22,23,27,28)(24,32,35,29)(25,30,36,39)(26,31,38,40)(33,44,46,41)(34,45,48,42)(37,43,49,50)(47,52,53,51);(22,24,27,35)(23,29,28,32)(25,33,36,46)(26,34,38,48)(30,41,39,44)(31,42,40,45)(37,47,49,53)(43,51,50,52);(14,16,17,20)(15,19,18,21)(22,25)(23,30)(24,33)(26,37)(27,36)(28,39)(29,41)(31,43)(32,44)(34,47)(35,46)(38,49)(40,50)(42,51)(45,52)(48,53);(22,26)(23,31)(24,34)(25,37)(27,38)(28,40)(29,42)(30,43)(32,45)(33,47)(35,48)(36,49)(39,50)(41,51)(44,52)(46,53)1066 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 55838);