Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #120 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C32 · Schur multiplier (H2) = C28×C3 |
| direct product | C22×C32×#125 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C24×C32 | C23 |
| commutator, Frattini, cosocle | C22 | C25×C32 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C24×C32 ◁ G | |
3576 conjugacy classes of subgroups.
| minimal degree | μ(G) = 26 |
| transitive degree | μt(G) = 1152 |
A minimal faithful permutation representation — 5 generators on 26 points:
(1,2)(21,22,23);(3,4)(24,25,26);(7,11)(9,12)(13,14,16,18)(15,17,19,20);(5,6,8,10)(7,9,11,12)(13,14)(15,17)(16,18)(19,20);(5,7)(6,9)(8,11)(10,12)(13,15,16,19)(14,17,18,20)504 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 4497);