Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C23×C3×C4 |
No aliases for this group.
| Sylow | C32 ⋊ #2381 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×C3⋊D3 |
| commutator | C22×C32 | C23×C4 |
| Fitting | C32×#383 | C2 |
| socle, prime radical, cosocle | C23×C32 | C24 |
| hypercenter | #383 | C3⋊D3 |
| hypocenter | C32 | #2381 |
| LCS | G ▷ C22×C32 ▷ C32 | |
| UCS | C1 ◁ C23 ◁ #383 | |
1272 conjugacy classes of subgroups; only the 337 normal subgroups are shown.
This group has 1272 conjugacy classes of subgroups — too many to draw. Only its 337 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1152 |
Polycyclic presentation:
2^7,3^2|a^2=g,b^2=e,c^2=ef,d^2=e,b^a=be,c^a=cf,d^a=def,c^b=cef,d^b=de,h^b=h^2,i^b=i^2150 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 41960);