Finite Group DatabasebetaFinite Group Databasebeta| order | 8384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Sylow | C131 ⋊ #379 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C22×D131 |
| commutator | C22×C131 | C22×C4 |
| Fitting | C25×C131 | C2 |
| socle | C23×C131 | C23 |
| hypercenter | C25 | D131 |
| hypocenter | C131 | #379 |
| LCS | G ▷ C22×C131 ▷ C131 | |
| UCS | C1 ◁ C23 ◁ C25 | |
506 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,131|a^2=f,b^a=bd,c^a=ce,g^a=g^1302108 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C131⋊#1304, #30665875, #30665876, … |
| maximal normal subgroup of | C131⋊#1304, #30665875, #30665876, … |
| maximal quotient of | #30664184, #30664202, #30664232, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8384, 405);