Finite Group DatabasebetaFinite Group Databasebeta| order | 8768 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | #95×C137 ⋊ C2 |
| Sylow | C137 ⋊ #396 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C22×D137 |
| commutator, socle | C23×C137 | C23 |
| Fitting | #95×C137 | C2 |
| hypercenter | #95 | D137 |
| hypocenter | C137 | #396 |
| LCS | G ▷ C23×C137 ▷ C137 | |
| UCS | C1 ◁ C23 ◁ #95 | |
186 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,137|a^2=de,b^2=d,b^a=bd,c^a=ce,g^a=g^136,c^b=cf,g^b=g^136,g^c=g^1361382 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #396×D137, C2×#22577327, #31784026, … |
| maximal normal subgroup of | #396×D137, C2×#22577327, #31784026, … |
| maximal quotient of | #31779033, #31779040, #31779051, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8768, 473);