Finite Group DatabasebetaFinite Group Databasebeta| order | 8416 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C24×C263 ⋊ C2 |
| Sylow | C263 ⋊ #120 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×D263 |
| commutator, socle | C22×C263 | C23 |
| Fitting | C24×C263 | C2 |
| hypercenter | C24 | D263 |
| hypocenter | C263 | #120 |
| LCS | G ▷ C22×C263 ▷ C263 | |
| UCS | C1 ◁ C22 ◁ C24 | |
130 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,263|b^a=bd,c^a=ce,f^a=f^2622110 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #30682124, #120×D263, C2×#22554439, … |
| maximal normal subgroup of | #30682124, #120×D263, C2×#22554439, … |
| maximal quotient of | #30681794, #30681811, #30681817, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8416, 115);