Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C25 |
| direct product | C13×#19029 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C2×#120 |
| commutator, Frattini, cosocle | C42 | C24×C13 |
| prime radical | C13×#121 | D4 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C2×C42×C13 ◁ G | |
824 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)(14,15,19,17)(16,22,24,29)(18,26,28,21)(20,27,23,25)(32,38)(33,40)(35,43)(36,41)(39,42)(44,45);(14,16,19,24)(15,20,17,23)(18,27,28,25)(21,29,26,22)(30,31,34,37)(32,35,39,44)(33,41,40,36)(38,45,42,43);(14,17,19,15)(16,23,24,20)(18,21,28,26)(22,27,29,25)(30,32)(31,35)(33,42)(34,39)(36,45)(37,44)(38,40)(41,43);(16,24)(20,23)(22,29)(25,27)481 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 12017);