Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| isoclinism | isoclinic class of #92199 |
| automorphism | ? |
| homology | Abelianization (H1) = C8 · Schur multiplier (H2) = C3 |
No aliases for this group.
| derived, Sylow | #6857 ⋊ C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4 | #92199 |
| commutator, hypocenter | #6857 | C8 |
| Frattini | C33×C4 | C3⋊D3 |
| Fitting, cosocle | C4×#6857 | C2 |
| socle | C2×C32 | #1084 |
| prime radical | C2×C3×H(3,𝔽3) | Dic3 |
| LCS | G ▷ #6857 | |
| UCS | C1 ◁ C4 | |
184 conjugacy classes of subgroups; only the 37 normal subgroups are shown.
This group has 184 conjugacy classes of subgroups — too many to draw. Only its 37 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 648 |
Polycyclic presentation:
2^3,3^5|a^2=b,b^2=c,e^3=h,d^a=d^2,e^a=e^2h^2,f^a=fg^2h^2,g^a=g^2,h^a=h^2,e^d=ef,f^d=fh,f^e=fg88 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 53);