Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2×C34 |
No aliases for this group.
| Sylow | C35 ⋊ D4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C3⋊D3×C3⋊(C3⋊D3) |
| commutator, Fitting, socle, cosocle | C2×C35 | C22 |
| hypocenter | C35 | D4 |
| LCS | G ▷ C2×C35 ▷ C35 | |
| UCS | C1 ◁ C2 | |
7584 conjugacy classes of subgroups; only the 372 normal subgroups are shown.
This group has 7584 conjugacy classes of subgroups — too many to draw. Only its 372 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|a^2=c,b^a=bc,g^a=g^2,h^a=h^2,d^b=d^2,e^b=e^2,f^b=f^2177 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 3833);