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×#63064 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C26 |
| commutator, Frattini, cosocle | C22 | C26×C13 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ G | |
6286 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)(16,17,22,25)(18,21,26,27)(23,24,28,29)(30,31)(32,41)(33,34)(35,40)(36,37)(38,45)(39,46)(42,52)(43,55)(44,56)(47,48)(49,54)(50,51)(53,60)(57,59)(58,61);(15,20)(16,22)(21,27)(23,28)(31,37)(33,46)(38,41)(40,51)(42,55)(47,54)(53,56)(57,61);(14,16)(15,17)(18,23)(19,22)(20,25)(21,24)(26,28)(27,29)(30,32,36,45)(31,38,37,41)(33,42,46,55)(34,43,39,52)(35,44,50,60)(40,53,51,56)(47,57,54,61)(48,58,49,59);(14,17)(15,16)(18,24)(19,25)(20,22)(21,23)(26,29)(27,28)(30,33)(31,39)(32,42)(34,37)(35,47)(36,46)(38,52)(40,49)(41,43)(44,57)(45,55)(48,51)(50,54)(53,59)(56,58)(60,61);(14,18,19,26)(15,21,20,27)(16,23,22,28)(17,24,25,29)(30,34,36,39)(31,33,37,46)(32,43,45,52)(35,49,50,48)(38,42,41,55)(40,54,51,47)(44,59,60,58)(53,61,56,57);(30,35)(31,40)(32,44)(33,47)(34,48)(36,50)(37,51)(38,53)(39,49)(41,56)(42,57)(43,58)(45,60)(46,54)(52,59)(55,61)910 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 56052);