Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| isoclinism | isoclinic class of #14519184 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting, derived, Sylow | C32×H(3,𝔽3) ⋊ C23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C32×H(3,𝔽3) | C23 |
| Frattini | C3 | #10620215 |
| socle | C33 | C2×D32 |
| LCS | G ▷ C32×H(3,𝔽3) | |
| UCS | C1 | |
877 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 877 conjugacy classes of subgroups — too many to draw. Only its 58 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 36 |
Polycyclic presentation:
2^3,3^5|d^a=d^2,g^a=g^2,d^b=d^2,e^b=e^2,h^b=h^2,e^c=e^2,f^c=f^2,g^d=gh54 conjugacy classes — view the full character table.
| maximal subgroup of | D32×((C3⋊D3)⋊C3)⋊C2, #72224544, #72228685, … |
| maximal normal subgroup of | D32×((C3⋊D3)⋊C3)⋊C2, #72228685, #72259817, … |
| maximal quotient of | #72224536, #72228645, C3×#14519184 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 3578);