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×C9 |
| direct product | C23×#6896 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C32 | C33 |
| commutator, Frattini, cosocle | C32 | C23×C33 |
| prime radical | C23×C33 | C32 |
| LCS | G ▷ C32 ▷ C1 | |
| UCS | C1 ◁ C23×C32 ◁ G | |
960 conjugacy classes of subgroups.
| minimal degree | μ(G) = 24 |
| transitive degree | μt(G) = 648 |
A minimal faithful permutation representation — 3 generators on 24 points:
(1,2)(8,12,14)(9,13,15)(17,18,22)(20,23,21);(3,4)(7,8,13,11,14,15,10,12,9)(16,17,20,19,18,21,24,22,23);(5,6)(7,9,12,10,15,14,11,13,8)(16,18,23,19,22,20,24,17,21)408 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 2958);