Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Sylow | C32 ⋊ #2868 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C22×D32 |
| commutator, socle, prime radical, cosocle | C23×C32 | C24 |
| Fitting | C2×C32×C42 | C22 |
| hypercenter | C2×C42 | D32 |
| hypocenter | C32 | #2868 |
| LCS | G ▷ C23×C32 ▷ C32 | |
| UCS | C1 ◁ C23 ◁ C2×C42 | |
1389 conjugacy classes of subgroups; only the 428 normal subgroups are shown.
This group has 1389 conjugacy classes of subgroups — too many to draw. Only its 428 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 384 |
Polycyclic presentation:
2^7,3^2|a^2=e,b^2=e,c^2=f,d^2=g,b^a=be,c^a=cf,d^a=dg,h^a=h^2,i^a=i^2,i^b=hi^2,i^d=hi^2168 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 91101);