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×#62890 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C26 |
| commutator, Frattini, cosocle | C22 | C26×C13 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ G | |
6276 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)(30,31,36,40)(32,41,37,33)(34,38,48,54)(35,49,50,39)(42,52,46,44)(43,45,51,55)(47,59,60,53)(56,57,58,61);(15,20)(16,22)(21,27)(23,28)(30,32,36,37)(31,33,40,41)(34,46,48,42)(35,43,50,51)(38,52,54,44)(39,45,49,55)(47,58,60,56)(53,61,59,57);(14,16)(15,17)(18,23)(19,22)(20,25)(21,24)(26,28)(27,29)(30,32)(31,33)(34,42)(35,43)(36,37)(38,44)(39,45)(40,41)(46,48)(47,56)(49,55)(50,51)(52,54)(53,57)(58,60)(59,61);(14,17)(15,16)(18,24)(19,25)(20,22)(21,23)(26,29)(27,28)(30,33)(31,37)(32,40)(34,44)(35,45)(36,41)(38,46)(39,51)(42,54)(43,49)(47,57)(48,52)(50,55)(53,58)(56,59)(60,61);(30,34,36,48)(31,38,40,54)(32,42,37,46)(33,44,41,52)(35,47,50,60)(39,53,49,59)(43,56,51,58)(45,57,55,61);(14,18,19,26)(15,21,20,27)(16,23,22,28)(17,24,25,29)(30,35,36,50)(31,39,40,49)(32,43,37,51)(33,45,41,55)(34,47,48,60)(38,53,54,59)(42,56,46,58)(44,57,52,61)910 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 55878);