Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| automorphism | ? |
| homology | Abelianization (H1) = C8 · Schur multiplier (H2) = C3 |
No aliases for this group.
| Fitting, derived, Sylow | H(5,𝔽3) ⋊ C8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, socle, hypercenter | C3 | #10620193 |
| commutator, Fitting, hypocenter | H(5,𝔽3) | C8 |
| prime radical | #92404 | C4 |
| cosocle | #11758052 | C2 |
| LCS | G ▷ H(5,𝔽3) | |
| UCS | C1 ◁ C3 | |
181 conjugacy classes of subgroups.
| minimal degree | μ(G) = 27 |
| transitive degree | μt(G) = 27 |
Polycyclic presentation:
2^3,3^5|a^2=b,b^2=c,d^a=de,e^a=d,f^a=g,g^a=fg^2,d^b=d^2e,e^b=de,f^b=fg^2,g^b=f^2g^2,d^c=d^2,e^c=e^2,f^c=f^2,g^c=g^2,g^d=gh,f^e=fh,g^e=gh^234 conjugacy classes — view the full character table.
| maximal subgroup of | #72221926, C2×#14519085, #72254096, … |
| maximal normal subgroup of | #72221926, C2×#14519085, #72254096, … |
| maximal quotient of | C2×#14519085 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 3479);