Finite Group DatabasebetaFinite Group Databasebeta| order | 1088 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×M16×C17 ⋊ C2 |
| Sylow | C17 ⋊ #568 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C4 | C23×D17 |
| commutator, socle | C2×C17 | C23×C4 |
| Fitting | C2×M16×C17 | C2 |
| prime radical | C2×#63252 | C2 |
| cosocle | C4×C17 | C24 |
| hypercenter | C2×M16 | D17 |
| hypocenter | C17 | #568 |
| LCS | G ▷ C2×C17 ▷ C17 | |
| UCS | C1 ◁ C4 ◁ C2×M16 | |
258 conjugacy classes of subgroups; only the 147 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 147 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 272 |
Polycyclic presentation:
2^6,17|a^2=e,e^2=f,d^a=df,c^b=cf,g^c=g^16194 conjugacy classes — view the full character table.
| maximal subgroup of | #14529002, #14529005, #14529021, … |
| maximal normal subgroup of | #14529002, #14529005, #14529021, … |
| maximal quotient of | #14537201, #14537202, #14537209, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1088, 1315);