Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C28×C3 |
No aliases for this group.
| Fitting | C32×#379 ⋊ C2 |
| Sylow | C32 ⋊ #2403 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×C3⋊D3 |
| commutator, socle, cosocle | C23×C32 | C24 |
| Fitting | C32×#379 | C2 |
| hypercenter | #379 | C3⋊D3 |
| hypocenter | C32 | #2403 |
| LCS | G ▷ C23×C32 ▷ C32 | |
| UCS | C1 ◁ C23 ◁ #379 | |
4692 conjugacy classes of subgroups; only the 425 normal subgroups are shown.
This group has 4692 conjugacy classes of subgroups — too many to draw. Only its 425 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 288 |
Polycyclic presentation:
2^7,3^2|b^a=be,c^a=cf,d^a=de,h^a=h^2,i^a=i^2,c^b=cg,h^c=h^2,i^c=i^2150 conjugacy classes — view the full character table.
| maximal subgroup of | #72252259, C3⋊D3×#2403 |
| maximal normal subgroup of | #72252259, C3⋊D3×#2403 |
| maximal quotient of | #72214782, #72215029 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 43003);