Finite Group DatabasebetaFinite Group Databasebeta| order | 1088 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C17 ⋊ #504 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C22×#3633 |
| commutator, socle | C2×C17 | C22×C8 |
| Fitting | D4×C17 | C8 |
| prime radical | #63254 | C4 |
| cosocle | #3624 | C23 |
| hypercenter | D4 | #3633 |
| hypocenter | C17 | #504 |
| LCS | G ▷ C2×C17 ▷ C17 | |
| UCS | C1 ◁ C2 ◁ D4 | |
84 conjugacy classes of subgroups.
| transitive degree | μt(G) = 544 |
Polycyclic presentation:
2^6,17|a^2=d,d^2=e,e^2=f,g^a=g^9,c^b=cf,g^d=g^13,g^e=g^1650 conjugacy classes — view the full character table.
| maximal subgroup of | #14546001, #14546002, #14546004, … |
| maximal normal subgroup of | #14546001, #14546002, #14546004, … |
| maximal quotient of | #14545945, #14545946, #14545954, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1088, 1670);