Finite Group DatabasebetaFinite Group Databasebeta| order | 1088 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C17 ⋊ #435 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×#595 |
| commutator, socle | C22×C17 | C22×C4 |
| Fitting, prime radical | C2×D4×C17 | C4 |
| cosocle | C2×Dic17 | C23 |
| hypercenter | C2×D4 | #595 |
| hypocenter | C17 | #435 |
| LCS | G ▷ C22×C17 ▷ C17 | |
| UCS | C1 ◁ C22 ◁ C2×D4 | |
124 conjugacy classes of subgroups; only the 48 normal subgroups are shown.
This group has 124 conjugacy classes of subgroups — too many to draw. Only its 48 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 544 |
Polycyclic presentation:
2^6,17|a^2=e,c^2=e,e^2=f,b^a=bd,c^a=cf,g^a=g^4,g^c=g^13,g^e=g^1668 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#11763840, D17⋊#435, #14545498, … |
| maximal normal subgroup of | C2×#11763840, D17⋊#435, #14545498, … |
| maximal quotient of | #14544385, #14544389, #14544393, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1088, 1580);