Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C26 · Schur multiplier (H2) = C214×C3 |
No aliases for this group.
| Fitting | C32×#585 ⋊ C2 |
| Sylow | C32 ⋊ 2−1+6 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C25×C3⋊D3 |
| commutator, socle, cosocle | C2×C32 | C26 |
| Fitting | C32×#585 | C2 |
| hypercenter | #585 | C3⋊D3 |
| hypocenter | C32 | 2−1+6 |
| LCS | G ▷ C2×C32 ▷ C32 | |
| UCS | C1 ◁ C2 ◁ #585 | |
17388 conjugacy classes of subgroups; only the 4701 normal subgroups are shown.
This group has 17388 conjugacy classes of subgroups — too many to draw. Only its 4701 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|c^2=g,d^2=g,b^a=bg,f^a=fg,e^b=eg,d^c=dg,h^e=h^2,i^e=i^2,h^f=h^2,i^f=i^2201 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 153301);