Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | #6896 ⋊ Q8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #92308⋊C2 |
| commutator, Fitting, cosocle | C2×#6896 | C22 |
| Frattini, socle | C2×C32 | #1113 |
| prime radical | C2×C33 | D32 |
| hypocenter | #6896 | Q8 |
| LCS | G ▷ C2×#6896 ▷ #6896 | |
| UCS | C1 ◁ C2 | |
150 conjugacy classes of subgroups.
| transitive degree | μt(G) = 72 |
Polycyclic presentation:
2^3,3^5|a^2=c,b^2=c,e^3=h,f^3=g^2,b^a=bc,d^a=d^2,f^a=f^2g,g^a=g^2,d^b=d^2,e^b=e^2h^2,h^b=h^2,e^d=eg,f^d=fh^257 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 1522);