Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C24×C4 |
| unambiguous semidirect product | Dic83⋊#95 |
| Sylow | C83 ⋊ C4⋊#95 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C24 | C22×D83 |
| commutator | C22×C83 | C2×C42 |
| Fitting | C2×#95×C83 | C2 |
| socle, prime radical, cosocle | C24×C83 | C23 |
| hypercenter | C2×#95 | D83 |
| hypocenter | C83 | C4⋊#95 |
| LCS | G ▷ C22×C83 ▷ C83 | |
| UCS | C1 ◁ C24 ◁ C2×#95 | |
656 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,83|a^2=f,b^2=g,c^2=e,b^a=bd,c^a=ce,h^c=h^821696 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35297125, #35297126, #35297130, … |
| maximal normal subgroup of | #35297125, #35297126, #35297130, … |
| maximal quotient of | #35292323, #35292330, #35310189, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 2738);