Finite Group DatabasebetaFinite Group Databasebeta| order | 8336 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | C4⋊Dic521 |
| Sylow | C521 ⋊ C4⋊C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C2×D521 |
| commutator | C2×C521 | C2×C4 |
| Fitting | C2×C4×C521 | C2 |
| socle | C22×C521 | C22 |
| hypercenter | C2×C4 | D521 |
| hypocenter | C521 | C4⋊C4 |
| LCS | G ▷ C2×C521 ▷ C521 | |
| UCS | C1 ◁ C22 ◁ C2×C4 | |
26 conjugacy classes of subgroups.
Polycyclic presentation:
2^4,521|a^2=d,b^2=c,b^a=bc,e^a=e^5202090 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #30659629, #30659630, #30659632, … |
| maximal normal subgroup of | #30659629, #30659630, #30659632, … |
| maximal quotient of | #30659615, C4⋊#16861960, #30659640, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8336, 20);