Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | #391×C83 ⋊ C2 |
| Sylow | C83 ⋊ #2337 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D83 |
| commutator | C22×C83 | C23×C4 |
| Fitting | #391×C83 | C2 |
| socle, cosocle | C23×C83 | C24 |
| prime radical | C22×D332 | C22 |
| hypercenter | #391 | D83 |
| hypocenter | C83 | #2337 |
| LCS | G ▷ C22×C83 ▷ C83 | |
| UCS | C1 ◁ C23 ◁ #391 | |
540 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,83|a^2=g,b^2=eg,c^2=e,d^2=ef,b^a=be,c^a=cf,d^a=de,c^b=ce,h^b=h^82,h^c=h^82,h^d=h^821192 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #2337×D83, C2×#24910275, #35563326, … |
| maximal normal subgroup of | #2337×D83, C2×#24910275, #35563326, … |
| maximal quotient of | #35325677, #35325736, #35325742, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 7322);