Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #60756 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C13 · Schur multiplier (H2) = C28 |
| direct product | C13×#60999 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C13 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C4×C13×#41 ◁ G | |
1682 conjugacy classes of subgroups.
| minimal degree | μ(G) = 61 |
| transitive degree | μt(G) = 1664 |
A minimal faithful permutation representation — 5 generators on 61 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15)(16,22)(17,21)(18,20)(19,23)(24,28)(25,27)(26,29)(30,31)(32,37)(33,44)(34,39)(35,48)(36,40)(38,45)(41,56)(42,51)(43,52)(46,54)(47,53)(49,55)(50,59)(57,60)(58,61);(14,16)(15,19)(17,24)(18,23)(20,22)(21,26)(25,29)(27,28)(30,32,36,43)(31,37,40,52)(33,41,46,58)(34,47,35,42)(38,50,55,60)(39,53,48,51)(44,56,54,61)(45,59,49,57);(16,23)(19,22)(24,29)(26,28)(30,33,36,46)(31,38,40,55)(32,41,43,58)(34,45,35,49)(37,50,52,60)(39,54,48,44)(42,57,47,59)(51,56,53,61);(15,20)(19,22)(21,27)(26,28)(30,34,36,35)(31,39,40,48)(32,42,43,47)(33,45,46,49)(37,51,52,53)(38,54,55,44)(41,57,58,59)(50,56,60,61);(14,17,18,25)(15,21,20,27)(16,24,23,29)(19,26,22,28)(32,43)(37,52)(41,58)(42,47)(50,60)(51,53)(56,61)(57,59)637 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 53987);