Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C83 ⋊ #1840 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22×C4 | C22×D83 |
| commutator, socle, prime radical | C23×C83 | C22×C4 |
| Fitting | #376×C83 | C2 |
| cosocle | C22×C4×C83 | C23 |
| hypercenter | #376 | D83 |
| hypocenter | C83 | #1840 |
| LCS | G ▷ C23×C83 ▷ C83 | |
| UCS | C1 ◁ C22×C4 ◁ #376 | |
196 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,83|a^2=f,b^2=de,c^2=d,f^2=g,b^a=bd,c^a=ce,h^a=h^82,c^b=cg1684 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #1840×D83, C2×#24907608, #35404655, … |
| maximal normal subgroup of | #1840×D83, C2×#24907608, #35404655, … |
| maximal quotient of | #35298132, #35310013, #35312852, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 4655);