Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #24986 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C23 |
| direct product | C13×#29233 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C13 | #555 |
| commutator, Frattini, cosocle | C22×C4 | C24×C13 |
| socle | C2×C13 | #2572 |
| prime radical | C13×#575 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C13 ◁ C22×C4×C13 ◁ G | |
532 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)(14,15,19,24,20,25,18,23)(16,26,30,37,28,41,29,21)(17,31,33,40,34,22,35,39)(27,38,32,45,43,42,44,36);(14,16)(15,21,25,37)(17,32,34,44)(18,29)(19,30)(20,28)(22,38)(23,41,24,26)(27,33,43,35)(31,42)(36,40)(39,45);(14,17)(15,22)(16,27)(18,33)(19,35)(20,34)(21,36)(23,39)(24,40)(25,31)(26,42)(28,43)(29,32)(30,44)(37,45)(38,41);(15,23,25,24)(16,28)(21,26,37,41)(22,39,31,40)(27,43)(29,30)(32,44)(36,42,45,38)520 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 22221);