Finite Group DatabasebetaFinite Group Databasebeta| order | 8768 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C137 ⋊ #336 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22×C4 | C2×D137 |
| commutator | C2×C137 | C4×C8 |
| Fitting | C22×C8×C137 | C2 |
| socle | C23×C137 | C2×C4 |
| hypercenter | C22×C8 | D137 |
| hypocenter | C137 | #336 |
| LCS | G ▷ C2×C137 ▷ C137 | |
| UCS | C1 ◁ C22×C4 ◁ C22×C8 | |
118 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,137|a^2=d,b^2=e,d^2=f,b^a=bc,g^b=g^1362216 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #336×D137, C2×#22577157, #31780481, … |
| maximal normal subgroup of | #336×D137, C2×#22577157, #31780481, … |
| maximal quotient of | #31778616, #31778617, #31778619, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8768, 303);