Finite Group DatabasebetaFinite Group Databasebeta| order | 10688 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C167 ⋊ #568 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C4 | C23×D167 |
| commutator, socle | C2×C167 | C23×C4 |
| Fitting, prime radical | C2×#41×C167 | C2 |
| cosocle | C4×C167 | C24 |
| hypercenter | C2×#41 | D167 |
| hypocenter | C167 | #568 |
| LCS | G ▷ C2×C167 ▷ C167 | |
| UCS | C1 ◁ C4 ◁ C2×#41 | |
258 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,167|a^2=e,e^2=f,d^a=df,g^a=g^166,c^b=cf1694 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #36324357, #36324360, #36324376, … |
| maximal normal subgroup of | #36324357, #36324360, #36324376, … |
| maximal quotient of | #36332557, #36332566, #36332583, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10688, 1316);