Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #10304 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C13 · Schur multiplier (H2) = C2×C4 |
| direct product | C13×#10682 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C13 | #127 |
| commutator, Frattini, cosocle | C2×C42 | C23×C13 |
| LCS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C13 ◁ C2×C42×C13 ◁ G | |
394 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 3328 |
A minimal faithful permutation representation — 3 generators on 45 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,17,19)(16,20,21,18)(23,26)(27,28)(30,31,35,36,34,39,33,38)(32,40,43,37,42,45,41,44);(14,16,17,21)(15,18,19,20)(22,23,24,26)(25,27,29,28)(31,36)(33,35)(37,40)(38,39)(41,43)(44,45);(23,27)(25,29)(26,28)(30,32,34,42)(31,37,39,44)(33,43,35,41)(36,40,38,45)676 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 3670);