Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #9331 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C13 · Schur multiplier (H2) = C23 |
| direct product | C13×#9342 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | #386 |
| commutator | C22×C4 | C22×C4×C13 |
| Frattini, cosocle | C23×C4 | C23×C13 |
| prime radical | C24×C13 | C2×D4 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C23×C4×C13 ◁ G | |
478 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 832 |
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)(16,19,23,27)(17,24,25,20)(18,21)(22,26)(28,29)(30,31,34,38,35,39,33,37)(32,40,42,36,43,44,41,45);(14,16)(15,19,21,27)(17,22)(18,23)(20,26,24,29)(25,28)(30,32)(31,36)(33,42)(34,41)(35,43)(37,44)(38,40)(39,45);(14,17,18,25)(15,20,21,24)(16,22,23,28)(19,26,27,29)(30,32)(31,36)(33,41)(34,42)(35,43)(37,40)(38,44)(39,45)442 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 2330);