Finite Group DatabasebetaFinite Group Databasebeta| order | 8384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22 |
| direct product | Q8×C131⋊C8 |
| Sylow | C131 ⋊ C8×Q8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C4 | C22×D131 |
| commutator | C2×C131 | C22×C8 |
| Fitting | C4×Q8×C131 | C2 |
| socle | C22×C131 | C22×C4 |
| hypercenter | C4×Q8 | D131 |
| hypocenter | C131 | C8×Q8 |
| LCS | G ▷ C2×C131 ▷ C131 | |
| UCS | C1 ◁ C2×C4 ◁ C4×Q8 | |
102 conjugacy classes of subgroups.
1340 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #30664758, SD16×C131⋊C8, #30664765, … |
| maximal normal subgroup of | #30664758, SD16×C131⋊C8, #30664765, … |
| maximal quotient of | C4⋊C4×C131⋊C8, #30666520, #30666680, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8384, 675);