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×#63053 |
| 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)(16,17)(18,22)(19,20)(21,25)(23,24)(26,27)(28,29)(31,36)(37,47)(38,48)(39,49)(50,58)(51,59)(52,53)(60,61);(15,20)(16,21)(22,27)(23,28)(31,36)(32,40)(38,48)(39,49)(41,54)(42,55)(52,53)(56,57);(14,16,19,21)(15,17,20,25)(18,23,26,28)(22,24,27,29)(30,31)(32,37)(33,38)(34,39)(35,36)(40,47)(41,50)(42,51)(43,52)(44,48)(45,53)(46,49)(54,58)(55,59)(56,60)(57,61);(14,17)(15,21)(16,20)(18,24)(19,25)(22,28)(23,27)(26,29)(30,32)(31,37)(33,41)(34,42)(35,40)(36,47)(38,50)(39,51)(43,56)(44,54)(45,57)(46,55)(48,58)(49,59)(52,60)(53,61);(14,18,19,26)(15,22,20,27)(16,23,21,28)(17,24,25,29)(30,33,35,44)(31,38,36,48)(32,41,40,54)(34,45,46,43)(37,50,47,58)(39,53,49,52)(42,57,55,56)(51,61,59,60);(30,34,35,46)(31,39,36,49)(32,42,40,55)(33,43,44,45)(37,51,47,59)(38,52,48,53)(41,56,54,57)(50,60,58,61)910 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 56041);