Finite Group DatabasebetaFinite Group Databasebeta| order | 1088 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C4⋊C4×C17 ⋊ C4 |
| Sylow | C17 ⋊ #387 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×#595 |
| commutator, socle | C22×C17 | C22×C4 |
| Fitting | C4⋊C4×C17 | C4 |
| prime radical, cosocle | C22×D17 | C23 |
| hypercenter | C4⋊C4 | #595 |
| hypocenter | C17 | #387 |
| LCS | G ▷ C22×C17 ▷ C17 | |
| UCS | C1 ◁ C22 ◁ C4⋊C4 | |
154 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 154 conjugacy classes of subgroups — too many to draw. Only its 54 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 272 |
Polycyclic presentation:
2^6,17|a^2=f,b^2=f,c^2=d,b^a=bd,c^a=ce,g^a=g^4,g^b=g^13,g^f=g^1668 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#11763758, #14545238, #14545243, … |
| maximal normal subgroup of | C2×#11763758, #14545238, #14545243, … |
| maximal quotient of | #14543959, #14543963, #14543964, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1088, 1498);