Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #10012 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C13 · Schur multiplier (H2) = C23 |
| direct product | C13×#10035 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C13 | #127 |
| commutator, Frattini, cosocle | C2×C42 | C23×C13 |
| socle | C22×C13 | #392 |
| prime radical | C13×#532 | C22 |
| LCS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C13 ◁ C2×C42×C13 ◁ G | |
498 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 1664 |
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)(16,22)(17,25)(18,21)(19,24)(20,27)(23,29)(26,28)(30,31,35,39)(32,40,43,44)(33,38,34,37)(36,42,45,41);(19,28)(22,29)(30,32,35,43)(31,36,39,45)(33,42,34,41)(37,44,38,40);(14,16)(15,19)(17,26)(18,23)(20,29)(21,28)(22,25)(24,27)(32,41)(33,34)(36,40)(37,38)(42,43)(44,45)520 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 3023);