Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| isoclinism | isoclinic class of #548⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C32 · Schur multiplier (H2) = C22×C3 |
| direct product | C3×#3480⋊C3 |
| unambiguous semidirect product | #3480⋊C32 |
| unambiguous semidirect product | (C3×#3480)⋊C3 |
| Fitting | C3×#3480 ⋊ C3 |
| Sylow | #3480 ⋊ C32 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C3×C4 | C22×A4 |
| commutator, cosocle | C2×Q8 | C23×C32 |
| Frattini | C22 | C23×C3×A4 |
| Fitting | C3×#3480 | C3 |
| socle | C22×C3 | C23×A4 |
| hypercenter | C3×#117 | A4 |
| hypocenter | Q8 | C32×#41 |
| LCS | G ▷ C2×Q8 ▷ Q8 | |
| UCS | C1 ◁ C2×C3×C4 ◁ C3×#117 | |
680 conjugacy classes of subgroups; only the 162 normal subgroups are shown.
This group has 680 conjugacy classes of subgroups — too many to draw. Only its 162 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 192 |
210 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 153741);