Finite Group DatabasebetaFinite Group Databasebeta| order | 8416 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C263 ⋊ C22⋊Q8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×D263 |
| commutator, socle | C22×C263 | C23 |
| Fitting | C22×C4×C263 | C2 |
| hypercenter | C22×C4 | D263 |
| hypocenter | C263 | C22⋊Q8 |
| LCS | G ▷ C22×C263 ▷ C263 | |
| UCS | C1 ◁ C22 ◁ C22×C4 | |
74 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,263|a^2=d,b^2=d,b^a=bd,c^a=ce,f^a=f^2622110 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #30681674, #30681676, #30682089, … |
| maximal normal subgroup of | #30681674, #30681676, #30682089, … |
| maximal quotient of | #30681798, #30681811, #30681822, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8416, 125);