Finite Group DatabasebetaFinite Group Databasebeta| order | 8416 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×#16862375 |
| Fitting | C2×D4×C263 ⋊ C2 |
| Sylow | C263 ⋊ C2×#41 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C22×D263 |
| commutator | C2×C263 | C24 |
| Frattini | C2 | C23×D263 |
| Fitting | C2×D4×C263 | C2 |
| socle | C22×C263 | C23 |
| hypercenter | C2×D4 | D263 |
| hypocenter | C263 | C2×#41 |
| LCS | G ▷ C2×C263 ▷ C263 | |
| UCS | C1 ◁ C22 ◁ C2×D4 | |
164 conjugacy classes of subgroups.
1330 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #30681910, #30681919, #30681931, … |
| maximal normal subgroup of | #30681910, #30681919, #30681931, … |
| maximal quotient of | C2×#22554426, C2×#22554428, C2×(C22⋊D263)⋊C4, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8416, 188);