Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23×C3 |
| direct product | C2×#11758087 |
| Fitting | C2×H(5,𝔽3) ⋊ C22 |
| derived, Sylow | H(5,𝔽3) ⋊ C23 |
| subgroup | G/H | |
|---|---|---|
| center, socle, hypercenter | C2×C3 | C3⋊D32 |
| commutator, cosocle, hypocenter | H(5,𝔽3) | C23 |
| Frattini | C3 | C2×C3⋊D32 |
| Fitting | C2×H(5,𝔽3) | C22 |
| LCS | G ▷ H(5,𝔽3) | |
| UCS | C1 ◁ C2×C3 | |
1556 conjugacy classes of subgroups; only the 118 normal subgroups are shown.
This group has 1556 conjugacy classes of subgroups — too many to draw. Only its 118 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 54 |
88 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#14519143, C2×#72212528, C2×#14519185 |
| maximal normal subgroup of | C2×#14519143, C2×#14519185 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 3723);