Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| isoclinism | isoclinic class of #14519084 |
| automorphism | ? |
| homology | Abelianization (H1) = C8 · Schur multiplier (H2) = C32 |
No aliases for this group.
| Fitting, derived, Sylow | H(5,𝔽3) ⋊ C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | H(5,𝔽3) | C8 |
| Frattini, socle | C3 | #10620193 |
| prime radical | #92404 | C4 |
| cosocle | #11758052 | C2 |
| LCS | G ▷ H(5,𝔽3) | |
| UCS | C1 | |
176 conjugacy classes of subgroups.
| minimal degree | μ(G) = 54 |
| transitive degree | μt(G) = 54 |
Polycyclic presentation:
2^3,3^5|a^2=b,b^2=c,d^a=deh,e^a=dh^2,f^a=gh,g^a=fg^2h,h^a=h^2,d^b=d^2e,e^b=deh^2,f^b=fg^2,g^b=f^2g^2,d^c=d^2,e^c=e^2h^2,f^c=f^2,g^c=g^2h,e^d=eh,g^f=gh22 conjugacy classes — view the full character table.
| maximal subgroup of | #72214527, #72214583, #72228612, … |
| maximal normal subgroup of | #72214527, #72214583, #72228612, … |
| maximal quotient of | C2×#14519084 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 3478);