Finite Group DatabasebetaFinite Group Databasebeta| order | 1088 |
| isoclinism | isoclinic class of #595 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C2 |
No aliases for this group.
| derived, Sylow | C17 ⋊ C2×C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C16 | #595 |
| commutator, hypocenter | C17 | C2×C32 |
| Frattini | C8 | C2×#595 |
| Fitting | C16×C17 | C4 |
| socle | C2×C17 | C2×C16 |
| prime radical | C2×D17 | C16 |
| cosocle | #63214 | C22 |
| LCS | G ▷ C17 | |
| UCS | C1 ◁ C16 | |
34 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,g^a=g^13,g^b=g^16,g^c=g^16128 conjugacy classes — view the full character table.
| maximal subgroup of | C32×#595, #14543890, #14543933, … |
| maximal normal subgroup of | C32×#595, #14543890, #14543933, … |
| maximal quotient of | #14543889, #14543898, #14543942, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1088, 1480);