Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| isoclinism | isoclinic class of GO+(4,𝔽2) |
| automorphism | ? |
| homology | Abelianization (H1) = C82 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Sylow | C32 ⋊ #1273 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C42 | GO+(4,𝔽2) |
| commutator | C3⋊D3 | C82 |
| Fitting | C32×C42 | D4 |
| socle | C22×C32 | #95 |
| prime radical | C22×C3⋊D3 | C42 |
| cosocle | C42×C3⋊D3 | C22 |
| hypocenter | C32 | #1273 |
| LCS | G ▷ C3⋊D3 ▷ C32 | |
| UCS | C1 ◁ C42 | |
374 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 374 conjugacy classes of subgroups — too many to draw. Only its 91 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 192 |
Polycyclic presentation:
2^7,3^2|a^2=d,b^2=e,d^2=f,e^2=g,b^a=bc,i^a=hi^2,h^b=hi,i^b=hi^2,h^c=h^2,i^c=i^2,h^e=h^2,i^e=i^2144 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 4713);