Finite Group DatabasebetaFinite Group Databasebeta| order | 8608 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C269 ⋊ #108 |
| subgroup | G/H | |
|---|---|---|
| center | C4 | C22⋊D269 |
| commutator | C4×C269 | C2×C4 |
| Frattini | C2×C4 | C2×D269 |
| Fitting | M16×C269 | C2 |
| socle | C2×C269 | C4⋊C4 |
| hypercenter | M16 | D269 |
| hypocenter | C269 | #108 |
| LCS | G ▷ C4×C269 ▷ C2×C269 ▷ C269 | |
| UCS | C1 ◁ C4 ◁ C2×C4 ◁ M16 | |
30 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,269|a^2=d,b^2=c,c^2=e,d^2=e,b^a=bc,c^a=ce,f^b=f^2681354 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #108×D269, C2×#22575388, #31770652, … |
| maximal normal subgroup of | #108×D269, C2×#22575388, #31770652, … |
| maximal quotient of | #31770355, #31770357, #31770369, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8608, 81);