Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23472 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C24 |
| direct product | C13×#23834 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C13 | C2×#124 |
| commutator, Frattini, cosocle | C22×C4 | C24×C13 |
| socle | C2×C13 | #2398 |
| prime radical | C13×#575 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C13 ◁ C22×C8×C13 ◁ G | |
608 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 416 |
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)(16,25,28,38)(17,22)(18,23)(19,33)(20,24)(21,29,35,26)(27,39,42,44)(30,36)(31,37)(32,43)(34,41,45,40);(16,26,28,29)(17,30)(21,25,35,38)(22,36)(27,41,42,40)(31,32)(34,44,45,39)(37,43);(14,16)(15,21)(17,27)(18,26)(19,29)(20,28)(22,34)(23,38)(24,35)(25,33)(30,42)(31,40)(32,41)(36,45)(37,44)(39,43);(14,17,18,31,20,30,19,32)(15,22,23,37,24,36,33,43)(16,27,26,40,28,42,29,41)(21,34,38,44,35,45,25,39)598 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 16822);