Finite Group DatabasebetaFinite Group Databasebeta| order | 8608 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C269 ⋊ #101 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | #16864379 |
| commutator | C22×C269 | C2×C4 |
| Frattini | C2×C4 | C2×D269 |
| Fitting | M16×C269 | C2 |
| socle | C2×C269 | C22⋊C4 |
| hypercenter | M16 | D269 |
| hypocenter | C269 | #101 |
| LCS | G ▷ C22×C269 ▷ C2×C269 ▷ C269 | |
| UCS | C1 ◁ C2 ◁ C2×C4 ◁ M16 | |
38 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,269|a^2=d,b^2=e,d^2=e,b^a=bc,c^a=ce,d^b=de,f^b=f^2681351 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #101×D269, C2×#22575371, #31770586, … |
| maximal normal subgroup of | #101×D269, C2×#22575371, #31770586, … |
| maximal quotient of | #31770330, #31770346, #31770350, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8608, 64);