Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C2 |
| direct product | C3×#85552 |
| subgroup | G/H | |
|---|---|---|
| center, socle, hypercenter | C22×C3 | #1020 |
| commutator, cosocle, hypocenter | Q8⋊SL(2,𝔽3) | C2×C3 |
| Frattini | C22 | C3×#1020 |
| Fitting | C3×Q82 | D3 |
| prime radical | C3×Q8⋊SL(2,𝔽3) | C2 |
| LCS | G ▷ Q8⋊SL(2,𝔽3) | |
| UCS | C1 ◁ C22×C3 | |
202 conjugacy classes of subgroups; only the 26 normal subgroups are shown.
This group has 202 conjugacy classes of subgroups — too many to draw. Only its 26 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 384 |
69 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 157112);