Finite Group DatabasebetaFinite Group Databasebeta| order | 8384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | C131⋊#401 |
| Sylow | C131 ⋊ #401 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C22×D131 |
| commutator, socle | C23×C131 | C23 |
| Fitting | #95×C131 | C2 |
| hypercenter | #95 | D131 |
| hypocenter | C131 | #401 |
| LCS | G ▷ C23×C131 ▷ C131 | |
| UCS | C1 ◁ C23 ◁ #95 | |
118 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,131|a^2=def,b^2=de,c^2=d,b^a=bd,c^a=ce,c^b=cf,g^c=g^1301322 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #401×D131, C2×C131⋊#401, #30669258, … |
| maximal normal subgroup of | #401×D131, C2×C131⋊#401, #30669258, … |
| maximal quotient of | #30664221, #30664222, #30664223, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8384, 492);