Finite Group DatabasebetaFinite Group Databasebeta| order | 10688 |
| isoclinism | isoclinic class of D167 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C26 |
| direct product | C22×C8×D167 |
| Fitting | C22×C8×C167 ⋊ C2 |
| derived, Sylow | C167 ⋊ C23×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C8 | D167 |
| commutator, hypocenter | C167 | C23×C8 |
| Frattini | C4 | C23×D167 |
| Fitting | C22×C8×C167 | C2 |
| socle | C23×C167 | C2×C4 |
| prime radical | C23×D167 | C4 |
| cosocle | C4×C167 | C24 |
| LCS | G ▷ C167 | |
| UCS | C1 ◁ C22×C8 | |
338 conjugacy classes of subgroups.
2720 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #336×D167, #36323833, #340×D167, … |
| maximal normal subgroup of | #336×D167, #36323833, #340×D167, … |
| maximal quotient of | C2×C4×C8×D167, C22×C8×Dic167, C2×C22⋊C8×D167, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10688, 1305);