Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18446 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C25 |
| direct product | C13×#18453 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C13 |
| prime radical | C13×#3536 | C2 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C23×C4×C13 ◁ G | |
970 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)(16,19)(17,20)(18,21)(22,28)(23,26)(24,27)(25,29)(30,31,35,38)(32,39,41,44)(33,37,34,42)(36,43,45,40);(14,16)(15,19)(17,22)(18,23)(20,25)(21,26)(24,29)(27,28)(30,32,35,41)(31,36,38,45)(33,40,34,43)(37,44,42,39);(14,17)(15,20)(16,22)(18,24)(19,25)(21,27)(23,29)(26,28)(33,34)(37,42)(39,44)(40,43);(15,21)(19,26)(20,27)(25,28)(30,33,35,34)(31,37,38,42)(32,40,41,43)(36,44,45,39)442 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 11441);