Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18346 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C25 |
| direct product | C13×#18353 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C13 |
| prime radical | C22×D4×C13 | D4 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C23×C4×C13 ◁ G | |
946 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)(14,15,19,22)(16,23,26,29)(17,21,18,27)(20,24,28,25)(30,31)(32,35)(33,36)(34,37)(38,44)(39,42)(40,43)(41,45);(14,16,19,26)(15,20,22,28)(17,25,18,24)(21,29,27,23)(30,32)(31,35)(33,38)(34,39)(36,41)(37,42)(40,45)(43,44);(30,33)(31,36)(32,38)(34,40)(35,41)(37,43)(39,45)(42,44);(14,17,19,18)(15,21,22,27)(16,24,26,25)(20,23,28,29)(31,37)(35,42)(36,43)(41,44)442 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 11341);