Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #10046 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C13 · Schur multiplier (H2) = C22 |
| direct product | C13×#10582 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C13 | #120 |
| commutator, Frattini, cosocle | C2×C42 | C23×C13 |
| LCS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C13 ◁ C2×C42×C13 ◁ G | |
426 conjugacy classes of subgroups.
| minimal degree | μ(G) = 37 |
| transitive degree | μt(G) = 3328 |
A minimal faithful permutation representation — 3 generators on 37 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,18,20)(16,21,17,19)(22,23,25,28)(24,29,26,27)(30,31)(32,33)(34,36)(35,37);(14,16,18,17)(15,19,20,21)(22,24,25,26)(23,27,28,29)(30,32,35,36)(31,33,37,34);(14,17,18,16)(15,19,20,21)(23,27)(24,26)(28,29)(31,32)(33,34)(36,37)598 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 3570);