Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2×C3 |
No aliases for this group.
| Fitting, derived, Sylow | H(5,𝔽3) ⋊ C2×C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, socle, hypercenter | C3 | #10620198 |
| commutator, Fitting, hypocenter | H(5,𝔽3) | C2×C4 |
| prime radical | #11758087 | C2 |
| cosocle | #92404 | C22 |
| LCS | G ▷ H(5,𝔽3) | |
| UCS | C1 ◁ C3 | |
320 conjugacy classes of subgroups.
| minimal degree | μ(G) = 54 |
| transitive degree | μt(G) = 54 |
Polycyclic presentation:
2^3,3^5|a^2=c,d^a=de,e^a=de^2h^2,f^a=fg,g^a=fg^2h^2,d^b=d^2,e^b=e^2h,d^c=d^2,e^c=e^2h,f^c=f^2,g^c=g^2h,e^d=eh,g^f=gh40 conjugacy classes — view the full character table.
| derived subgroup of | #72228630 |
| maximal subgroup of | #72214495, #72214570, #72214583, … |
| maximal normal subgroup of | #72214495, #72214570, #72214583, … |
| maximal quotient of | #72228655, #72276096, #72276140 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 3499);