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×C33 |
| direct product | D4×#6891 |
| unambiguous semidirect product | C4⋊(C2×#6891) |
| subgroup | G/H | |
|---|---|---|
| center, commutator, Frattini, socle, cosocle | C2×C32 | C22×C33 |
| prime radical | C34×D4 | C3 |
| LCS | G ▷ C2×C32 ▷ C1 | |
| UCS | C1 ◁ C2×C32 ◁ G | |
1008 conjugacy classes of subgroups; only the 270 normal subgroups are shown.
This group has 1008 conjugacy classes of subgroups — too many to draw. Only its 270 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 22 |
| transitive degree | μt(G) = 108 |
A minimal faithful permutation representation — 3 generators on 22 points:
(1,2,3,4)(5,6,8,7,10,12,11,9,13)(14,15,17)(16,19,21)(18,22,20);(2,4)(6,9,10)(8,12,13);(15,18,19)(17,21,22)255 conjugacy classes — view the full character table.
| Fitting subgroup of | D4×#92302, D4×#92259, D4×#4169⋊C3, … |
| maximal subgroup of | D4×#10624749, D4×#92302, D4×#92259, … |
| maximal normal subgroup of | D4×#10624749, D4×#92302, D4×#92259, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 2200);