Finite Group DatabasebetaFinite Group Databasebeta| order | 8416 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C4⋊C4×C263 ⋊ C2 |
| Sylow | C263 ⋊ #117 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×D263 |
| commutator | C2×C263 | C22×C4 |
| Fitting | C4⋊C4×C263 | C2 |
| socle | C22×C263 | C23 |
| hypercenter | C4⋊C4 | D263 |
| hypocenter | C263 | #117 |
| LCS | G ▷ C2×C263 ▷ C263 | |
| UCS | C1 ◁ C22 ◁ C4⋊C4 | |
76 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,263|a^2=e,c^2=d,b^a=bd,f^b=f^262,f^c=f^2621330 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #30681931, #30681933, #30681941, … |
| maximal normal subgroup of | #30681931, #30681933, #30681941, … |
| maximal quotient of | #30681783, #30681785, C4⋊C4×Dic263, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8416, 104);