Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #17577 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C13 · Schur multiplier (H2) = C25 |
| direct product | C13×#17677 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C22×C22⋊C4 |
| commutator | C2×C4 | C23×C4×C13 |
| Frattini, cosocle | C42 | C24×C13 |
| prime radical | C13×#3444 | C2 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C22×C42×C13 ◁ G | |
976 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 832 |
A minimal faithful permutation representation — 4 generators on 45 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,18,22,19,23,17,21)(16,24,25,29,26,20,27,28)(30,31)(32,40,42,45)(33,38)(34,39)(35,37)(36,41,44,43);(14,16)(15,20)(17,25)(18,27)(19,26)(21,28)(22,29)(23,24)(30,32)(31,36)(33,41)(34,43)(35,42)(37,44)(38,40)(39,45);(14,17,19,18)(15,21,23,22)(16,25,26,27)(20,28,24,29)(31,37)(36,44)(38,39)(40,45);(14,17,19,18)(15,22,23,21)(16,25,26,27)(20,29,24,28)(30,33,35,34)(31,38,37,39)(32,41,42,43)(36,40,44,45)676 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 10665);