Finite Group DatabasebetaFinite Group Databasebeta| order | 8608 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D269⋊C16 |
| derived, Sylow | C269 ⋊ C2×C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C8 | #11761640 |
| commutator, hypocenter | C269 | C2×C16 |
| Frattini | C4 | C2×#11761640 |
| Fitting | C8×C269 | C4 |
| socle | C2×C269 | C2×C8 |
| LCS | G ▷ C269 | |
| UCS | C1 ◁ C8 | |
28 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,269|a^2=c,c^2=d,d^2=e,f^a=f^187,f^b=f^268,f^c=f^268568 conjugacy classes — view the full character table.
| maximal subgroup of | C16×#11761640, #31771492, #31771517, … |
| maximal normal subgroup of | C16×#11761640, #31771492, #31771517, … |
| maximal quotient of | #31771491, #31771500, #31771526, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8608, 219);