Finite Group DatabasebetaFinite Group Databasebeta| order | 8768 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C137 ⋊ #340 |
| subgroup | G/H | |
|---|---|---|
| center | C23 | D548 |
| commutator | C4×C137 | C42 |
| Frattini | C22×C4 | C2×D137 |
| Fitting | C22×C8×C137 | C2 |
| socle | C23×C137 | D4 |
| hypercenter | C22×C8 | D137 |
| hypocenter | C137 | #340 |
| LCS | G ▷ C4×C137 ▷ C2×C137 ▷ C137 | |
| UCS | C1 ◁ C23 ◁ C22×C4 ◁ C22×C8 | |
114 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,137|a^2=d,b^2=e,c^2=f,e^2=f,b^a=bc,c^a=cf,e^a=ef,g^a=g^1362204 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #31778798, #31778799, #31778801, … |
| maximal normal subgroup of | #31778798, #31778799, #31778801, … |
| maximal quotient of | #31778624, #31778629, #31778648, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8768, 312);