Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of D4×C32⋊H(3,𝔽3) |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C33 · Schur multiplier (H2) = C2×C3 |
| direct product | D4×#6900 |
| unambiguous semidirect product | C4⋊(C2×#6900) |
| subgroup | G/H | |
|---|---|---|
| center, commutator, Frattini, socle, cosocle | C2×C32 | C22×C33 |
| prime radical | C33×D4 | C32 |
| LCS | G ▷ C2×C32 ▷ C1 | |
| UCS | C1 ◁ C2×C32 ◁ G | |
560 conjugacy classes of subgroups.
| minimal degree | μ(G) = 22 |
| transitive degree | μt(G) = 324 |
A minimal faithful permutation representation — 3 generators on 22 points:
(1,2,3,4)(6,8,11)(9,13,12)(15,17,20)(18,22,21);(2,4)(5,6,9,7,8,12,10,11,13);(14,15,18,16,17,21,19,20,22)255 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 2209);