Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #2613 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C32 · Schur multiplier (H2) = C24×C3 |
| direct product | C32×#2634 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C32 | C24 |
| commutator, Frattini, cosocle | C23 | C24×C32 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C32 ◁ G | |
1248 conjugacy classes of subgroups.
| minimal degree | μ(G) = 34 |
| transitive degree | μt(G) = 1152 |
A minimal faithful permutation representation — 4 generators on 34 points:
(1,2,3)(12,15)(16,18)(19,20,24,22)(21,27,29,25)(23,26,31,30)(28,33,34,32);(4,5,6)(8,10)(12,15)(16,18)(19,21,24,29)(20,25,22,27)(23,28,31,34)(26,32,30,33);(7,8)(9,10)(11,12)(13,16)(14,15)(17,18)(19,22,24,20)(21,25,29,27)(23,26,31,30)(28,33,34,32);(11,13,14,17)(12,16,15,18)(19,23)(20,26)(21,28)(22,30)(24,31)(25,32)(27,33)(29,34)288 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 3694);