Finite Group DatabasebetaFinite Group Databasebeta| order | 8384 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | C2×#16862293 |
| Fitting | C2×#41×C131 ⋊ C2 |
| Sylow | C131 ⋊ C2×2−1+4 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C23×D131 |
| commutator | C2×C131 | C25 |
| Frattini | C2 | C24×D131 |
| Fitting | C2×#41×C131 | C2 |
| socle | C22×C131 | C24 |
| hypercenter | C2×#41 | D131 |
| hypocenter | C131 | C2×2−1+4 |
| LCS | G ▷ C2×C131 ▷ C131 | |
| UCS | C1 ◁ C22 ◁ C2×#41 | |
794 conjugacy classes of subgroups.
1334 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #30665918, #30665921, #30665934, … |
| maximal normal subgroup of | #30665918, #30665921, #30665934, … |
| maximal quotient of | C2×#22553788, C2×#22553789, C2×#22553791, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8384, 1382);