Finite Group DatabasebetaFinite Group Databasebeta| order | 1088 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C17×C22⋊Q8 ⋊ C2 |
| Sylow | C17 ⋊ #554 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D17 |
| commutator, socle, cosocle | C22×C17 | C24 |
| Fitting | C17×C22⋊Q8 | C2 |
| prime radical | C2×C22⋊D17 | C22 |
| hypercenter | C22⋊Q8 | D17 |
| hypocenter | C17 | #554 |
| LCS | G ▷ C22×C17 ▷ C17 | |
| UCS | C1 ◁ C22 ◁ C22⋊Q8 | |
228 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 105 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 544 |
Polycyclic presentation:
2^6,17|a^2=e,b^2=ef,d^2=e,b^a=be,c^a=cf,d^b=de,g^d=g^16137 conjugacy classes — view the full character table.
| maximal subgroup of | D17×#554, C2×#11763513, #14542336, … |
| maximal normal subgroup of | D17×#554, C2×#11763513, #14542336, … |
| maximal quotient of | #14531656, #14531658, #14531682, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1088, 1253);