Finite Group DatabasebetaFinite Group Databasebeta| order | 10688 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22 |
| direct product | M32×D167 |
| Fitting | M32×C167 ⋊ C2 |
| Sylow | C167 ⋊ C2×M32 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C8 | C22×D167 |
| commutator, socle | C2×C167 | C22×C8 |
| Fitting | M32×C167 | C2 |
| prime radical | C22×D167 | C8 |
| cosocle | C8×C167 | C23 |
| hypercenter | M32 | D167 |
| hypocenter | C167 | C2×M32 |
| LCS | G ▷ C2×C167 ▷ C167 | |
| UCS | C1 ◁ C8 ◁ M32 | |
90 conjugacy classes of subgroups.
1700 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #347×D167, #36325741, #349×D167, … |
| maximal normal subgroup of | #347×D167, #36325741, #349×D167, … |
| maximal quotient of | #346×D167, M32×Dic167, #36325731, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10688, 962);