Finite Group DatabasebetaFinite Group Databasebeta| order | 1088 |
| isoclinism | isoclinic class of #3633 |
| 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 | C8 | #3633 |
| commutator, hypocenter | C17 | C2×C32 |
| Frattini | C4 | C2×#3633 |
| Fitting | C8×C17 | C8 |
| socle | C2×C17 | C2×C16 |
| prime radical | C2×D17 | C16 |
| cosocle | #63216 | C22 |
| LCS | G ▷ C17 | |
| UCS | C1 ◁ C8 | |
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^9,g^b=g^16,g^c=g^13,g^d=g^1680 conjugacy classes — view the full character table.
| maximal subgroup of | #14545868, #14545871, C2×#11763916, … |
| maximal normal subgroup of | #14545868, #14545871, C2×#11763916, … |
| maximal quotient of | #14545867, #14545877, #14545883, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1088, 1656);