Finite Group DatabasebetaFinite Group Databasebeta| order | 10688 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | #95×C167 ⋊ C2 |
| Sylow | C167 ⋊ #393 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C22×D167 |
| commutator, socle, cosocle | C23×C167 | C23 |
| Fitting | #95×C167 | C2 |
| prime radical | C23×D167 | C22 |
| hypercenter | #95 | D167 |
| hypocenter | C167 | #393 |
| LCS | G ▷ C23×C167 ▷ C167 | |
| UCS | C1 ◁ C23 ◁ #95 | |
202 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 202 conjugacy classes of subgroups — too many to draw. Only its 61 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^6,167|a^2=d,b^2=d,b^a=bd,c^a=ce,c^b=cf,g^b=g^166,g^c=g^1661682 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #36323091, #36323096, #36323119, … |
| maximal normal subgroup of | #36323091, #36323096, #36323119, … |
| maximal quotient of | #36322382, #36322384, #36322393, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10688, 462);