Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C28 |
| direct product | D9×#392 |
| Fitting | C9×#392 ⋊ C2 |
| Sylow | C9 ⋊ C2×#392 |
| subgroup | G/H | |
|---|---|---|
| center | C23 | C23×D9 |
| commutator, cosocle | C23×C9 | C24 |
| Frattini, socle | C23×C3 | C23×D3 |
| Fitting | C9×#392 | C2 |
| hypercenter | #392 | D9 |
| hypocenter | C9 | C2×#392 |
| LCS | G ▷ C23×C9 ▷ C9 | |
| UCS | C1 ◁ C23 ◁ #392 | |
2718 conjugacy classes of subgroups; only the 266 normal subgroups are shown.
This group has 2718 conjugacy classes of subgroups — too many to draw. Only its 266 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 288 |
132 conjugacy classes — view the full character table.
| maximal subgroup of | D9×#2403, D9×#2433, D9×#2669, … |
| maximal normal subgroup of | D9×#2403, D9×#2433, D9×#2669, … |
| maximal quotient of | D9×#1438, D9×#2021, C2×D9×#392 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 42089);