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×#62891 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C26 |
| commutator, Frattini, cosocle | C22 | C26×C13 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ G | |
6280 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)(14,15,19,20)(16,21,23,18)(17,25,27,22)(24,26,29,28)(30,31,36,41)(32,42,46,37)(33,34,39,38)(35,51,52,40)(43,44,47,49)(45,53,59,56)(48,54,55,50)(57,61,60,58);(15,20)(16,23)(22,25)(24,29)(30,32,36,46)(31,37,41,42)(33,43,39,47)(34,49,38,44)(35,45,52,59)(40,53,51,56)(48,57,55,60)(50,61,54,58);(14,16)(15,21)(17,24)(18,20)(19,23)(22,28)(25,26)(27,29)(30,32)(31,37)(33,47)(34,44)(35,45)(36,46)(38,49)(39,43)(40,53)(41,42)(48,60)(50,58)(51,56)(52,59)(54,61)(55,57);(14,17,19,27)(15,22,20,25)(16,24,23,29)(18,26,21,28)(30,33,36,39)(31,38,41,34)(32,43,46,47)(35,48,52,55)(37,44,42,49)(40,54,51,50)(45,57,59,60)(53,58,56,61);(30,34,36,38)(31,39,41,33)(32,44,46,49)(35,50,52,54)(37,43,42,47)(40,55,51,48)(45,58,59,61)(53,57,56,60);(14,18,19,21)(15,16,20,23)(17,26,27,28)(22,24,25,29)(30,35,36,52)(31,40,41,51)(32,45,46,59)(33,48,39,55)(34,50,38,54)(37,53,42,56)(43,57,47,60)(44,58,49,61)910 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 55879);