Finite Group DatabasebetaFinite Group Databasebeta| order | 10688 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Sylow | C167 ⋊ #379 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C22×D167 |
| commutator | C22×C167 | C22×C4 |
| Fitting, prime radical | C25×C167 | C2 |
| socle, cosocle | C23×C167 | C23 |
| hypercenter | C25 | D167 |
| hypocenter | C167 | #379 |
| LCS | G ▷ C22×C167 ▷ C167 | |
| UCS | C1 ◁ C23 ◁ C25 | |
506 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,167|a^2=f,b^a=bd,c^a=ce,g^a=g^1662684 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C167⋊#1304, #36324052, #36324053, … |
| maximal normal subgroup of | C167⋊#1304, #36324052, #36324053, … |
| maximal quotient of | #36322361, #36322379, #36322409, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10688, 405);