Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| isoclinism | isoclinic class of #92199 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2×C3 |
| direct product | C2×#11757322 |
| derived, Sylow | #6857 ⋊ C2×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | #92199 |
| commutator, hypocenter | #6857 | C2×C4 |
| Frattini | C2×C33 | C2×C3⋊D3 |
| Fitting | C22×#6857 | C2 |
| socle | C22×C32 | #272 |
| prime radical | C22×C3×H(3,𝔽3) | D3 |
| cosocle | C2×#6857 | C22 |
| LCS | G ▷ #6857 | |
| UCS | C1 ◁ C22 | |
368 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 63 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 648 |
88 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 550);