Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #60756 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C13 · Schur multiplier (H2) = C27×C4 |
| direct product | C13×#60834 |
| 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 | |
2104 conjugacy classes of subgroups.
| minimal degree | μ(G) = 37 |
| transitive degree | μt(G) = 832 |
A minimal faithful permutation representation — 5 generators on 37 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15)(16,20)(17,19)(18,21)(23,27)(24,30)(26,33)(28,36)(31,37)(32,34);(14,16,17,21)(15,18,19,20)(22,23)(24,31)(25,27)(26,29)(28,32)(30,36)(33,35)(34,37);(16,21)(18,20)(22,24)(23,28)(25,32)(26,34)(27,31)(29,36)(30,33)(35,37);(15,19)(18,20)(22,23)(24,28)(25,27)(26,29)(30,37)(31,32)(33,35)(34,36);(23,27)(28,31)(29,35)(36,37)637 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 53822);