Finite Group DatabasebetaFinite Group Databasebeta| order | 1088 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C17 ⋊ M64 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C4 | C2×#3633 |
| commutator, socle | C2×C17 | C2×C16 |
| Fitting | C2×C4×C17 | C8 |
| prime radical | C22×C17 | C16 |
| cosocle | #63216 | C22 |
| hypercenter | C2×C4 | #3633 |
| hypocenter | C17 | M64 |
| LCS | G ▷ C2×C17 ▷ C17 | |
| UCS | C1 ◁ C4 ◁ C2×C4 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 544 |
Polycyclic presentation:
2^6,17|a^2=c,c^2=d,d^2=e,e^2=f,b^a=bf,g^a=g^9,g^c=g^13,g^d=g^1656 conjugacy classes — view the full character table.
| maximal subgroup of | #14545872, #14545873, #14545878, … |
| maximal normal subgroup of | #14545872, #14545873, #14545878, … |
| maximal quotient of | #14545869, C22⋊#10587528, C4⋊#10587528, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1088, 1657);