Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| isoclinism | isoclinic class of #4207⋊C2 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C23 |
| direct product | C2×C3×#4207⋊C2 |
| Fitting | C2×C3×#737 ⋊ C22 |
| derived | #737 ⋊ C23×C3 |
| Sylow | C3×#737 ⋊ C23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | #4207⋊C2 |
| commutator, cosocle, hypocenter | #737 | C23×C3 |
| Frattini | C3 | C2×C3×#1113 |
| Fitting | C2×C3×#737 | C22 |
| socle | C2×C32 | #1113 |
| LCS | G ▷ #737 | |
| UCS | C1 ◁ C2×C3 | |
617 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 617 conjugacy classes of subgroups — too many to draw. Only its 82 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 108 |
126 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#72221848, C2×#72221852, C2×#72221853, … |
| maximal normal subgroup of | C2×#72221858 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 3712);