Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| isoclinism | isoclinic class of #14519140 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2×C3 |
No aliases for this group.
| Fitting, Sylow | H(5,𝔽3) ⋊ D4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, cosocle | #92404 | C22 |
| Frattini, socle | C3 | #10620206 |
| Fitting, hypocenter | H(5,𝔽3) | D4 |
| LCS | G ▷ #92404 ▷ H(5,𝔽3) | |
| UCS | C1 | |
390 conjugacy classes of subgroups; only the 12 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 12 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 27 |
| transitive degree | μt(G) = 27 |
Polycyclic presentation:
2^3,3^5|b^a=bc,d^a=d^2,f^a=f^2,g^a=f^2g,h^a=h^2,d^b=e^2,e^b=d^2,f^b=f^2g^2,h^b=h^2,d^c=d^2,e^c=e^2,f^c=f^2,g^c=g^2,g^d=gh^2,f^e=fh,g^e=gh^231 conjugacy classes — view the full character table.
| maximal subgroup of | #72210394, #72214527, #72214570, … |
| maximal normal subgroup of | #72210394, #72214527, #72214570, … |
| maximal quotient of | C2×#14519140, #72228680 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 3534);