Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Sylow | C32 ⋊ #2492 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C22×D32 |
| commutator, socle, cosocle | C23×C32 | C24 |
| Fitting | C32×#95 | C22 |
| prime radical | C23×C3⋊D3 | C23 |
| hypercenter | #95 | D32 |
| hypocenter | C32 | #2492 |
| LCS | G ▷ C23×C32 ▷ C32 | |
| UCS | C1 ◁ C23 ◁ #95 | |
1111 conjugacy classes of subgroups.
| transitive degree | μt(G) = 192 |
Polycyclic presentation:
2^7,3^2|a^2=eg,b^2=ef,d^2=e,b^a=be,c^a=cf,d^a=de,c^b=cg,h^b=h^2,i^b=h^2i,h^c=h^2,i^c=i^2,i^d=hi^2108 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 53120);