Finite Group DatabasebetaFinite Group Databasebeta| order | 8608 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C8×C269 ⋊ C4 |
| Sylow | C269 ⋊ #107 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | C4⋊#11761640 |
| commutator | C4×C269 | C2×C4 |
| Frattini | C4 | C2×#11761640 |
| Fitting | C8×C269 | C4 |
| socle | C2×C269 | C4⋊C4 |
| hypercenter | C8 | #11761640 |
| hypocenter | C269 | #107 |
| LCS | G ▷ C4×C269 ▷ C2×C269 ▷ C269 | |
| UCS | C1 ◁ C2 ◁ C4 ◁ C8 | |
36 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,269|a^2=d,b^2=ce,c^2=e,b^a=bc,c^a=ce,f^a=f^187,f^d=f^268550 conjugacy classes — view the full character table.
| maximal subgroup of | #31771517, #31771518, #31771531, … |
| maximal normal subgroup of | #31771517, #31771518, #31771531, … |
| maximal quotient of | #31771468, #31771469, #31771479, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8608, 215);