Finite Group DatabasebetaFinite Group Databasebeta| order | 8768 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C2×C42 |
No aliases for this group.
| Sylow | C137 ⋊ #376 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4 | C2×D137 |
| commutator | C2×C137 | C2×C42 |
| Frattini | C23 | C22×D137 |
| Fitting | C2×C42×C137 | C2 |
| socle | C23×C137 | C23 |
| hypercenter | C2×C42 | D137 |
| hypocenter | C137 | #376 |
| LCS | G ▷ C2×C137 ▷ C137 | |
| UCS | C1 ◁ C22×C4 ◁ C2×C42 | |
178 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,137|a^2=e,b^2=f,c^2=d,b^a=bd,g^b=g^1362216 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #31778617, #31778681, #31778683, … |
| maximal normal subgroup of | #31778617, #31778681, #31778683, … |
| maximal quotient of | C4×#17983995, #31779014, #31779016, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8768, 395);