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×#63068 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C26 |
| commutator, Frattini, cosocle | C22 | C26×C13 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ G | |
6274 conjugacy classes of subgroups.
| minimal degree | μ(G) = 61 |
| transitive degree | μt(G) = 1664 |
A minimal faithful permutation representation — 6 generators on 61 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,20,19)(16,23,18,21)(17,22,27,26)(24,29,25,28)(30,31,36,40)(32,41,42,37)(33,38,46,52)(34,35,39,49)(43,54,56,50)(44,55,51,45)(47,48,53,59)(57,61,60,58);(14,16,20,18)(15,21,19,23)(17,25,27,24)(22,29,26,28)(32,42)(33,46)(37,41)(38,52)(44,51)(45,55)(47,53)(48,59);(14,17,20,27)(15,22,19,26)(16,24,18,25)(21,28,23,29)(30,32,36,42)(31,37,40,41)(33,43,46,56)(34,44,39,51)(35,45,49,55)(38,50,52,54)(47,57,53,60)(48,58,59,61);(14,18,20,16)(15,23,19,21)(17,25,27,24)(22,29,26,28)(30,33)(31,38)(32,43)(34,47)(35,48)(36,46)(37,50)(39,53)(40,52)(41,54)(42,56)(44,57)(45,58)(49,59)(51,60)(55,61);(14,19,20,15)(16,23,18,21)(17,26,27,22)(24,29,25,28)(30,34)(31,35)(32,44)(33,47)(36,39)(37,45)(38,48)(40,49)(41,55)(42,51)(43,57)(46,53)(50,58)(52,59)(54,61)(56,60);(30,35)(31,39)(32,45)(33,48)(34,40)(36,49)(37,51)(38,53)(41,44)(42,55)(43,58)(46,59)(47,52)(50,60)(54,57)(56,61)910 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 56056);