Finite Group DatabasebetaFinite Group Databasebeta| order | 8416 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C2×Dic263⋊C4 |
| Sylow | C263 ⋊ C2×C4⋊C4 |
| subgroup | G/H | |
|---|---|---|
| center | C23 | C2×D263 |
| commutator | C2×C263 | C22×C4 |
| Frattini | C22 | C22×D263 |
| Fitting | C22×C4×C263 | C2 |
| socle | C23×C263 | C22 |
| hypercenter | C22×C4 | D263 |
| hypocenter | C263 | C2×C4⋊C4 |
| LCS | G ▷ C2×C263 ▷ C263 | |
| UCS | C1 ◁ C23 ◁ C22×C4 | |
92 conjugacy classes of subgroups.
2116 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #30681663, #30681789, C4×Dic263⋊C4, … |
| maximal normal subgroup of | #30681663, #30681789, C4×Dic263⋊C4, … |
| maximal quotient of | C2×C263⋊#95, C4×Dic263⋊C4, #30681796, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8416, 100);