Finite Group DatabasebetaFinite Group Databasebeta| order | 8336 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C2×C4×C521 ⋊ C2 |
| Sylow | C521 ⋊ #41 |
| subgroup | G/H | |
|---|---|---|
| center | C4 | C2×D521 |
| commutator, socle | C2×C521 | C23 |
| Frattini | C2 | C22×D521 |
| Fitting | C2×C4×C521 | C2 |
| hypercenter | C2×C4 | D521 |
| hypocenter | C521 | #41 |
| LCS | G ▷ C2×C521 ▷ C521 | |
| UCS | C1 ◁ C4 ◁ C2×C4 | |
40 conjugacy classes of subgroups.
Polycyclic presentation:
2^4,521|c^2=d,b^a=bd,e^b=e^5202090 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #30659634, #30659636, #30659714, … |
| maximal normal subgroup of | #30659634, #30659636, #30659714, … |
| maximal quotient of | #30659665, #30659667, C4×C22⋊D521, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8336, 40);