Finite Group DatabasebetaFinite Group Databasebeta| order | 1088 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C17 ⋊ #383 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C22×D17 |
| commutator | C22×C17 | C22×C4 |
| Fitting | C17×#95 | C2 |
| socle, prime radical, cosocle | C23×C17 | C23 |
| hypercenter | #95 | D17 |
| hypocenter | C17 | #383 |
| LCS | G ▷ C22×C17 ▷ C17 | |
| UCS | C1 ◁ C23 ◁ #95 | |
138 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1088 |
Polycyclic presentation:
2^6,17|a^2=f,b^2=de,c^2=d,b^a=bd,c^a=ce,g^c=g^16188 conjugacy classes — view the full character table.
| maximal subgroup of | #14527329, #14527333, #14527358, … |
| maximal normal subgroup of | #14527329, #14527333, #14527358, … |
| maximal quotient of | #14527008, #14527009, #14527010, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1088, 416);