Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2×C3 |
No aliases for this group.
| derived, Sylow | H(5,𝔽3) ⋊ C2×C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, socle, hypercenter | C2×C3 | C3⋊D32 |
| commutator, hypocenter | H(5,𝔽3) | C2×C4 |
| Fitting, cosocle | C2×H(5,𝔽3) | C22 |
| prime radical | C2×#92392 | C2 |
| LCS | G ▷ H(5,𝔽3) | |
| UCS | C1 ◁ C2×C3 | |
836 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 836 conjugacy classes of subgroups — too many to draw. Only its 100 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 108 |
Polycyclic presentation:
2^3,3^5|b^2=c,f^a=f^2,g^a=g^2,d^b=d^2,e^b=e^2,e^d=eh,g^f=gh88 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 3205);