Finite Group DatabasebetaFinite Group Databasebeta| order | 8768 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C137 ⋊ #405 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C4 | C22×D137 |
| commutator | C2×C137 | C2×C42 |
| Fitting | #117×C137 | C2 |
| socle | C22×C137 | C22×C4 |
| hypercenter | #117 | D137 |
| hypocenter | C137 | #405 |
| LCS | G ▷ C2×C137 ▷ C137 | |
| UCS | C1 ◁ C2×C4 ◁ #117 | |
130 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,137|a^2=d,b^2=e,d^2=f,g^a=g^136,c^b=cf1400 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #31780543, #31780588, #31780591, … |
| maximal normal subgroup of | #31780543, #31780588, #31780591, … |
| maximal quotient of | #31779070, #31779073, #31779079, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8768, 505);