Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #392 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C13 · Schur multiplier (H2) = C23 |
| direct product | C13×#21676 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C8×C13 | C23 |
| commutator | C23 | C23×C4×C13 |
| Frattini, cosocle | C22×C4 | C24×C13 |
| socle, prime radical | C23×C13 | C23×C4 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C22×C8×C13 ◁ G | |
658 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 3328 |
A minimal faithful permutation representation — 4 generators on 45 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15)(16,20)(17,21)(18,19)(22,23)(24,26)(25,27)(28,29)(30,31,36,39,35,38,33,34)(32,40,41,42,43,37,44,45);(15,19)(20,21)(22,24,25,28)(23,26,27,29)(30,32)(31,37)(33,44)(34,42)(35,43)(36,41)(38,40)(39,45);(14,16,18,17)(15,20,19,21)(23,27)(26,29)(30,33,35,36)(31,34,38,39)(32,41,43,44)(37,45,40,42);(14,17,18,16)(15,21,19,20)(30,34,33,38,35,39,36,31)(32,42,44,40,43,45,41,37)1144 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 14664);