Finite Group DatabasebetaFinite Group Databasebeta| order | 8416 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C263 ⋊ #108 |
| subgroup | G/H | |
|---|---|---|
| center | C4 | D1052 |
| commutator | C4×C263 | C2×C4 |
| Frattini | C2×C4 | C2×D263 |
| Fitting | C2×C8×C263 | C2 |
| socle | C2×C263 | C4⋊C4 |
| hypercenter | C2×C8 | D263 |
| hypocenter | C263 | #108 |
| LCS | G ▷ C4×C263 ▷ C2×C263 ▷ C263 | |
| UCS | C1 ◁ C4 ◁ C2×C4 ◁ C2×C8 | |
30 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,263|a^2=d,b^2=c,c^2=e,d^2=e,b^a=bc,c^a=ce,f^a=f^2622110 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #30681745, #30681746, #30681751, … |
| maximal normal subgroup of | #30681745, #30681746, #30681751, … |
| maximal quotient of | #30681689, #30681691, #30681703, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8416, 82);