Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2×C32 |
No aliases for this group.
| Sylow | C32×H(3,𝔽3) ⋊ D4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2×C3 | D3×C3⋊(C3⋊D3) |
| commutator, Fitting, cosocle | C2×C32×H(3,𝔽3) | C22 |
| socle | C2×C33 | C2×C3⋊D3 |
| hypocenter | C32×H(3,𝔽3) | D4 |
| LCS | G ▷ C2×C32×H(3,𝔽3) ▷ C32×H(3,𝔽3) | |
| UCS | C1 ◁ C2×C3 | |
1435 conjugacy classes of subgroups; only the 154 normal subgroups are shown.
This group has 1435 conjugacy classes of subgroups — too many to draw. Only its 154 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
Polycyclic presentation:
2^3,3^5|a^2=c,b^a=bc,g^a=g^2,d^b=d^2,e^b=e^2,f^b=f^2,f^e=fh117 conjugacy classes — view the full character table.
| maximal subgroup of | #72229131, #67×C3⋊#272, #72259785, … |
| maximal normal subgroup of | #67×C3⋊#272, #72259785, #72260006 |
| maximal quotient of | #72229131 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 3179);