Finite Group DatabasebetaFinite Group Databasebeta| order | 8608 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C269 ⋊ #131 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C22×#11761640 |
| commutator, socle | C2×C269 | C22×C4 |
| Fitting | Q8×C269 | C4 |
| hypercenter | Q8 | #11761640 |
| hypocenter | C269 | #131 |
| LCS | G ▷ C2×C269 ▷ C269 | |
| UCS | C1 ◁ C2 ◁ Q8 | |
62 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,269|a^2=d,d^2=e,f^a=f^187,c^b=ce,f^b=f^268,f^c=f^268,f^d=f^268355 conjugacy classes — view the full character table.
| maximal subgroup of | #31771648, #31771649, #31771650, … |
| maximal normal subgroup of | #31771648, #31771649, #31771650, … |
| maximal quotient of | #31771570, #31771580, #31771612, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8608, 234);