Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Fitting | C2×C9×#120 ⋊ C2 |
| Sylow | C9 ⋊ #2403 |
| subgroup | G/H | |
|---|---|---|
| center | C23 | C23×D9 |
| commutator, cosocle | C23×C9 | C24 |
| Frattini, socle | C23×C3 | C23×D3 |
| Fitting | C2×C9×#120 | C2 |
| hypercenter | C2×#120 | D9 |
| hypocenter | C9 | #2403 |
| LCS | G ▷ C23×C9 ▷ C9 | |
| UCS | C1 ◁ C23 ◁ C2×#120 | |
2346 conjugacy classes of subgroups.
| transitive degree | μt(G) = 288 |
Polycyclic presentation:
2^7,3^2|h^3=i,b^a=be,c^a=cf,d^a=de,c^b=cg,h^b=h^2i^2,i^b=i^2150 conjugacy classes — view the full character table.
| maximal subgroup of | D9×#2403, #72268990 |
| maximal normal subgroup of | D9×#2403, #72268990 |
| maximal quotient of | #72268842, #72268866, #72268867, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 42996);