Finite Group DatabasebetaFinite Group Databasebeta| order | 8608 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C269 ⋊ #117 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×D269 |
| commutator | C2×C269 | C22×C4 |
| Fitting | C22⋊C4×C269 | C2 |
| socle | C22×C269 | C23 |
| hypercenter | C22⋊C4 | D269 |
| hypocenter | C269 | #117 |
| LCS | G ▷ C2×C269 ▷ C269 | |
| UCS | C1 ◁ C22 ◁ C22⋊C4 | |
76 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,269|a^2=e,c^2=d,b^a=bd,f^c=f^2681360 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #31770577, #117×D269, C2×#22575409, … |
| maximal normal subgroup of | #31770577, #117×D269, C2×#22575409, … |
| maximal quotient of | #31770450, C22⋊C4×Dic269, #31770456, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8608, 102);