Finite Group DatabasebetaFinite Group Databasebeta| order | 1088 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C17 ⋊ #568 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C4 | C23×D17 |
| commutator, socle | C2×C17 | C23×C4 |
| Fitting, prime radical | C2×#41×C17 | C2 |
| cosocle | C4×C17 | C24 |
| hypercenter | C2×#41 | D17 |
| hypocenter | C17 | #568 |
| LCS | G ▷ C2×C17 ▷ C17 | |
| UCS | C1 ◁ C4 ◁ C2×#41 | |
258 conjugacy classes of subgroups.
| transitive degree | μt(G) = 272 |
Polycyclic presentation:
2^6,17|a^2=e,e^2=f,d^a=df,g^a=g^16,c^b=cf194 conjugacy classes — view the full character table.
| maximal subgroup of | #14529003, #14529006, #14529022, … |
| maximal normal subgroup of | #14529003, #14529006, #14529022, … |
| maximal quotient of | #14537203, #14537212, #14537229, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1088, 1316);