Finite Group DatabasebetaFinite Group Databasebeta| order | 8384 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C131 ⋊ #405 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C4 | C22×D131 |
| commutator | C2×C131 | C2×C42 |
| Fitting | C2×M16×C131 | C2 |
| socle | C22×C131 | C22×C4 |
| hypercenter | C2×M16 | D131 |
| hypocenter | C131 | #405 |
| LCS | G ▷ C2×C131 ▷ C131 | |
| UCS | C1 ◁ C2×C4 ◁ C2×M16 | |
130 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,131|a^2=d,b^2=e,d^2=f,g^a=g^130,c^b=cf,g^b=g^1301340 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #30665715, #30665717, #30665760, … |
| maximal normal subgroup of | #30665715, #30665717, #30665760, … |
| maximal quotient of | M16×C131⋊C8, #30664245, #30664248, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8384, 507);