Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C22×#6860 ⋊ C2 |
| Sylow | #6860 ⋊ D4 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | C2×#6860⋊C2 |
| commutator, cosocle | C2×#6860 | C22 |
| Frattini | C2×C33 | C2×C3⋊D3 |
| Fitting | C22×#6860 | C2 |
| socle | C2×C32 | C2×#272 |
| hypercenter | C22 | #6860⋊C2 |
| hypocenter | #6860 | D4 |
| LCS | G ▷ C2×#6860 ▷ #6860 | |
| UCS | C1 ◁ C2 ◁ C22 | |
280 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 280 conjugacy classes of subgroups — too many to draw. Only its 39 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 324 |
Polycyclic presentation:
2^3,3^5|d^3=h^2,e^3=h^2,b^a=bc,d^a=d^2h,e^a=e^2h,f^a=fg^2h^2,g^a=g^2,h^a=h^2,e^d=ef,f^d=fh,f^e=fg79 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 557);