Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2×C3 |
No aliases for this group.
| Fitting | C22×#6911 ⋊ C2 |
| Sylow | #6911 ⋊ D4 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | C2×#92333 |
| commutator, cosocle | C2×#732 | C22×C3 |
| Frattini | C2×C32 | C2×C3×C3⋊D3 |
| Fitting | C22×#6911 | C2 |
| socle | C2×C3 | C2×C3×#272 |
| hypercenter | C22 | #92333 |
| hypocenter | #732 | C3×D4 |
| LCS | G ▷ C2×#732 ▷ #732 | |
| UCS | C1 ◁ C2 ◁ C22 | |
442 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 442 conjugacy classes of subgroups — too many to draw. Only its 57 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 108 |
Polycyclic presentation:
2^2,3,2,3^4|b^a=bd,e^a=e^2,f^a=f^2,h^a=h^2,f^c=fh,f^e=fg,g^e=gh,g^f=gh^297 conjugacy classes — view the full character table.
| maximal subgroup of | #72228545, D4×#92333, #72259411, … |
| maximal normal subgroup of | D4×#92333, #72259411, #72259417 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 2110);