Finite Group DatabasebetaFinite Group Databasebeta| order | 1088 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C17 ⋊ #346 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C4 | C2×#595 |
| commutator | C2×C17 | C4×C8 |
| Fitting | C42×C17 | C4 |
| socle, prime radical | C22×C17 | C2×C8 |
| cosocle | C2×#3622 | C22 |
| hypercenter | C42 | #595 |
| hypocenter | C17 | #346 |
| LCS | G ▷ C2×C17 ▷ C17 | |
| UCS | C1 ◁ C2×C4 ◁ C42 | |
54 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1088 |
Polycyclic presentation:
2^6,17|a^2=c,b^2=d,c^2=e,e^2=f,b^a=bf,g^a=g^13,g^c=g^16104 conjugacy classes — view the full character table.
| maximal subgroup of | #14543702, #14543736, #14543737, … |
| maximal normal subgroup of | #14543702, #14543736, #14543737, … |
| maximal quotient of | #14543696, #14543699, #14543822, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1088, 1437);