Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #10280 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C13 · Schur multiplier (H2) = C23 |
| direct product | C13×#10296 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | #392 |
| commutator, Frattini, cosocle | C2×C42 | C23×C13 |
| prime radical | C23×C13 | #120 |
| LCS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C2×C42×C13 ◁ G | |
504 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)(14,15,19,23)(16,24,17,21)(18,27,28,22)(20,26,29,25)(30,31)(32,35)(33,36)(34,38)(37,42)(39,43)(40,45)(41,44);(14,16,19,17)(15,20,23,29)(18,26,28,25)(21,27,24,22)(30,32,34,40)(31,35,38,45)(33,41,42,39)(36,44,37,43);(14,17,19,16)(15,21,23,24)(18,25,28,26)(20,22,29,27)(31,36)(33,42)(35,43)(37,38)(39,41)(44,45)520 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 3284);