Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| isoclinism | isoclinic class of #11757370 |
| automorphism | ? |
| homology | Abelianization (H1) = C8 · Schur multiplier (H2) = C3 |
No aliases for this group.
| derived, Sylow | #6856 ⋊ C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #11757370 |
| commutator, hypocenter | #6856 | C8 |
| Frattini | C2×C33 | #157 |
| Fitting, prime radical | C2×#6856 | C4 |
| socle | C2×C32 | #1088 |
| cosocle | #11757321 | C2 |
| LCS | G ▷ #6856 | |
| UCS | C1 ◁ C2 | |
83 conjugacy classes of subgroups.
| transitive degree | μt(G) = 72 |
Polycyclic presentation:
2^3,3^5|a^2=b,b^2=c,e^3=h^2,d^a=de,e^a=de^2f^2g,f^a=fg^2,g^a=g^2h^2,h^a=g^2h,d^b=d^2,e^b=e^2fgh^2,f^b=fh,g^b=g^2,h^b=h^2,e^d=ef,f^d=fg,f^e=fgh^240 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 105);