Finite Group DatabasebetaFinite Group Databasebeta| order | 8416 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C263 ⋊ #97 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C4 | C2×D263 |
| commutator | C2×C263 | C42 |
| Fitting | C2×C8×C263 | C2 |
| socle | C22×C263 | C2×C4 |
| hypercenter | C2×C8 | D263 |
| hypocenter | C263 | #97 |
| LCS | G ▷ C2×C263 ▷ C263 | |
| UCS | C1 ◁ C2×C4 ◁ C2×C8 | |
40 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,263|a^2=c,b^2=d,c^2=e,b^a=be,f^b=f^2622116 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #30681715, #97×D263, C2×#22554380, … |
| maximal normal subgroup of | #30681715, #97×D263, C2×#22554380, … |
| maximal quotient of | #30681659, #30681660, #30681692, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8416, 56);