Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of C32⋊H(3,𝔽3) |
| automorphism | ? |
| homology | Abelianization (H1) = C33×C8 · Schur multiplier (H2) = C3 |
| direct product | C8×#6900 |
| subgroup | G/H | |
|---|---|---|
| center | C32×C8 | C33 |
| commutator | C32 | C33×C8 |
| Frattini, cosocle | C32×C4 | C2×C33 |
| socle | C2×C32 | C33×C4 |
| prime radical | C2×C33 | C32×C4 |
| LCS | G ▷ C32 ▷ C1 | |
| UCS | C1 ◁ C32×C8 ◁ G | |
280 conjugacy classes of subgroups.
| minimal degree | μ(G) = 26 |
| transitive degree | μt(G) = 648 |
A minimal faithful permutation representation — 3 generators on 26 points:
(1,2,3,4,5,6,7,8)(10,12,15)(13,17,16)(19,21,24)(22,26,25);(9,10,13,11,12,16,14,15,17);(18,19,22,20,21,25,23,24,26)408 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 788);