Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C42 |
| direct product | C13×#15036 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C24×C13 | C24 |
| commutator, Frattini, cosocle | C24 | C24×C13 |
| LCS | G ▷ C24 ▷ C1 | |
| UCS | C1 ◁ C24×C13 ◁ G | |
1066 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 3328 |
A minimal faithful permutation representation — 4 generators on 45 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(15,18)(16,20)(22,23)(24,27)(25,26)(28,29)(30,31,33,35)(32,36,37,34)(39,40)(43,44);(15,18)(19,21)(23,26)(27,29)(38,39,42,40)(41,43,45,44);(14,15,17,18)(16,19,20,21)(22,23)(24,27)(25,26)(28,29)(30,32,33,37)(31,34,35,36)(38,40,42,39)(41,44,45,43);(14,16)(15,19)(17,20)(18,21)(22,24,25,28)(23,27,26,29)(30,31)(32,34)(33,35)(36,37)(38,41,42,45)(39,43,40,44)832 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 8024);