Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18618 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C25 |
| direct product | C13×#18677 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C2×#120 |
| commutator, Frattini, cosocle | C42 | C24×C13 |
| prime radical | C23×C13 | #120 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C2×C42×C13 ◁ G | |
858 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 1664 |
A minimal faithful permutation representation — 4 generators on 45 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,19,23)(16,24,27,28)(17,22,18,21)(20,25,29,26)(30,31)(32,39)(33,37)(34,42)(35,38)(36,40)(41,44)(43,45);(14,16,19,27)(15,20,23,29)(17,26,18,25)(21,24,22,28)(30,31)(32,36)(33,37)(34,42)(35,38)(39,43)(40,44)(41,45);(30,32,35,41)(31,36,38,45)(33,40,34,43)(37,44,42,39);(14,17,19,18)(15,21,23,22)(16,25,27,26)(20,28,29,24)(30,33,35,34)(31,37,38,42)(32,40,41,43)(36,44,45,39)598 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 11665);