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×#18362 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C13 |
| prime radical | C13×#534 | C22 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C2×C42×C13 ◁ G | |
910 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)(14,15,18,21)(16,22,23,29)(17,25,27,20)(19,26,28,24)(31,36)(33,34)(37,44)(38,39)(40,42)(43,45);(14,16)(15,19)(17,26)(18,23)(20,29)(21,28)(22,25)(24,27)(30,31)(32,37)(33,36)(34,38)(35,39)(40,43)(41,45)(42,44);(30,32)(31,37)(33,40)(34,42)(35,41)(36,43)(38,44)(39,45);(16,23)(19,28)(22,29)(24,26)(30,33,35,34)(31,38,39,36)(32,40,41,42)(37,44,45,43)442 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 11350);