Finite Group DatabasebetaFinite Group Databasebeta| order | 1088 |
| isoclinism | isoclinic class of #595 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C16 · Schur multiplier (H2) = C4 |
No aliases for this group.
| derived, Sylow | C17 ⋊ C4×C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C8 | #595 |
| commutator, hypocenter | C17 | C4×C16 |
| Frattini | C2×C4 | C2×#595 |
| Fitting | C2×C8×C17 | C4 |
| socle, prime radical | C22×C17 | C2×C8 |
| cosocle | C2×#3622 | C22 |
| LCS | G ▷ C17 | |
| UCS | C1 ◁ C2×C8 | |
58 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1088 |
Polycyclic presentation:
2^6,17|a^2=c,b^2=d,c^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 | C16×#3624, #14543695, #14543698, … |
| maximal normal subgroup of | C16×#3624, #14543695, #14543698, … |
| maximal quotient of | C8×#63216, #14543699, #14543823, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1088, 1435);