Finite Group DatabasebetaFinite Group Databasebeta| order | 1088 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22×C4 |
| unambiguous semidirect product | (C2×#595)⋊Q8 |
| Fitting | C2×Q8×C17 ⋊ C4 |
| Sylow | C17 ⋊ #391 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×#595 |
| commutator, socle | C22×C17 | C22×C4 |
| Fitting | C2×Q8×C17 | C4 |
| prime radical, cosocle | C22×D17 | C23 |
| hypercenter | C2×Q8 | #595 |
| hypocenter | C17 | #391 |
| LCS | G ▷ C22×C17 ▷ C17 | |
| UCS | C1 ◁ C22 ◁ C2×Q8 | |
186 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 186 conjugacy classes of subgroups — too many to draw. Only its 64 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=f,b^2=def,c^2=e,b^a=bd,c^a=ce,g^a=g^4,g^b=g^13,g^f=g^1668 conjugacy classes — view the full character table.
| maximal subgroup of | #14543880, #14544631, #14544740, … |
| maximal normal subgroup of | #14543880, #14544631, #14544740, … |
| maximal quotient of | #14543961, #14543963, #14543969, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1088, 1502);