Finite Group DatabasebetaFinite Group Databasebeta| order | 8384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C22×Dic524 |
| Sylow | C131 ⋊ C22×Q16 |
| subgroup | G/H | |
|---|---|---|
| center | C23 | D524 |
| commutator | C4×C131 | C24 |
| Frattini | C4 | C23×D131 |
| Fitting | C22×C8×C131 | C2 |
| socle | C23×C131 | D4 |
| hypercenter | C22×C8 | D131 |
| hypocenter | C131 | C22×Q16 |
| LCS | G ▷ C4×C131 ▷ C2×C131 ▷ C131 | |
| UCS | C1 ◁ C23 ◁ C22×C4 ◁ C22×C8 | |
258 conjugacy classes of subgroups.
2108 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #30666301, #30666303, #30666820, … |
| maximal normal subgroup of | #30666301, #30666303, #30666820, … |
| maximal quotient of | C22×#16862171, C22×#16862180, C2×C4×Dic524, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8384, 1326);