Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of C32⋊H(3,𝔽3) |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C33 · Schur multiplier (H2) = C23×C36 |
| direct product | C23×C32⋊H(3,𝔽3) |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C32 | C33 |
| commutator, Frattini, cosocle | C32 | C23×C33 |
| LCS | G ▷ C32 ▷ C1 | |
| UCS | C1 ◁ C23×C32 ◁ G | |
3024 conjugacy classes of subgroups.
| minimal degree | μ(G) = 24 |
| transitive degree | μt(G) = 216 |
A minimal faithful permutation representation — 3 generators on 24 points:
(1,2)(7,8,10)(9,12,14)(11,15,13)(16,17,19)(18,21,23)(20,24,22);(3,4)(8,11,12)(10,14,15);(5,6)(17,20,21)(19,23,24)408 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 2952);