Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #9239 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C13 · Schur multiplier (H2) = C23 |
| direct product | C13×#9250 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | #386 |
| commutator | C22×C4 | C22×C4×C13 |
| Frattini, cosocle | C2×C42 | C23×C13 |
| prime radical | C23×C13 | C4×D4 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C2×C42×C13 ◁ G | |
434 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)(14,15,20,23)(16,19,22,18)(17,24)(21,25)(26,28)(27,29)(30,31,34,39,35,38,33,37)(32,36,40,43,41,44,42,45);(14,16,18,15,20,22,19,23)(17,24,26,21,27,29,25,28)(30,32,33,40,35,41,34,42)(31,36,39,45,38,44,37,43);(14,17)(15,21)(16,24)(18,26)(19,25)(20,27)(22,29)(23,28)(30,33,35,34)(31,37,38,39)(32,40,41,42)(36,43,44,45)559 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 2238);