Finite Group DatabasebetaFinite Group Databasebeta| order | 8608 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C2×C8×C269 ⋊ C2 |
| Sylow | C269 ⋊ #102 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | D1076 |
| commutator | C4×C269 | C2×C4 |
| Frattini | C2×C4 | C2×D269 |
| Fitting | C2×C8×C269 | C2 |
| socle | C22×C269 | D4 |
| hypercenter | C2×C8 | D269 |
| hypocenter | C269 | #102 |
| LCS | G ▷ C4×C269 ▷ C2×C269 ▷ C269 | |
| UCS | C1 ◁ C22 ◁ C2×C4 ◁ C2×C8 | |
50 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,269|a^2=d,c^2=e,b^a=bc,c^a=ce,f^a=f^268,c^b=ce,f^b=f^2682158 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #102×D269, C2×#22575375, #31770600, … |
| maximal normal subgroup of | #102×D269, C2×#22575375, #31770600, … |
| maximal quotient of | #31770334, #31770340, #31770348, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8608, 68);