Finite Group DatabasebetaFinite Group Databasebeta| order | 8608 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C22⋊C4×C269 ⋊ C2 |
| Sylow | C269 ⋊ #123 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×D269 |
| commutator, socle | C22×C269 | C23 |
| Fitting | C22⋊C4×C269 | C2 |
| hypercenter | C22⋊C4 | D269 |
| hypocenter | C269 | #123 |
| LCS | G ▷ C22×C269 ▷ C269 | |
| UCS | C1 ◁ C22 ◁ C22⋊C4 | |
78 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,269|c^2=d,b^a=bd,c^a=ce,f^a=f^268,f^c=f^2681354 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #31770796, #123×D269, C2×#22575437, … |
| maximal normal subgroup of | #31770796, #123×D269, C2×#22575437, … |
| maximal quotient of | #31770466, #31770480, #31770482, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8608, 130);