Finite Group DatabasebetaFinite Group Databasebeta| order | 10688 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | 2−1+4×D167 |
| Fitting | 2−1+4×C167 ⋊ C2 |
| Sylow | C167 ⋊ C2×2−1+4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C24×D167 |
| commutator, socle, cosocle | C2×C167 | C25 |
| Fitting | 2−1+4×C167 | C2 |
| hypercenter | 2−1+4 | D167 |
| hypocenter | C167 | C2×2−1+4 |
| LCS | G ▷ C2×C167 ▷ C167 | |
| UCS | C1 ◁ C2 ◁ 2−1+4 | |
794 conjugacy classes of subgroups.
1445 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #454×D167, #456×D167, #36333499, … |
| maximal normal subgroup of | #454×D167, #456×D167, #36333499, … |
| maximal quotient of | #519×D167, #520×D167, #36337347, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10688, 1381);