Finite Group DatabasebetaFinite Group Databasebeta| order | 8768 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | C4⋊#14555513 |
| Sylow | C137 ⋊ C4⋊C16 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C4 | C2×#10587739 |
| commutator | C2×C137 | C2×C16 |
| Fitting | C42×C137 | C4 |
| socle | C22×C137 | C2×C8 |
| hypercenter | C42 | #10587739 |
| hypocenter | C137 | C4⋊C16 |
| LCS | G ▷ C2×C137 ▷ C137 | |
| UCS | C1 ◁ C2×C4 ◁ C42 | |
50 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,137|a^2=d,b^2=c,d^2=e,e^2=f,b^a=bc,g^a=g^100,g^d=g^136584 conjugacy classes — view the full character table.
| maximal subgroup of | D4⋊#14555513, #31795740, #31795741, … |
| maximal normal subgroup of | D4⋊#14555513, #31795740, #31795741, … |
| maximal quotient of | #31795811, #31795818, #31795827, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8768, 1469);