Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×#123×C83 ⋊ C2 |
| Sylow | C83 ⋊ #2464 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D83 |
| commutator, socle, cosocle | C23×C83 | C24 |
| Fitting | C2×#123×C83 | C2 |
| hypercenter | C2×#123 | D83 |
| hypocenter | C83 | #2464 |
| LCS | G ▷ C23×C83 ▷ C83 | |
| UCS | C1 ◁ C23 ◁ C2×#123 | |
710 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,83|b^2=e,d^2=ef,b^a=be,c^a=cf,d^a=de,c^b=cg,h^b=h^82,h^d=h^821186 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #2464×D83, C2×#24911466, #35572322, … |
| maximal normal subgroup of | #2464×D83, C2×#24911466, #35572322, … |
| maximal quotient of | #35326501, #35326693, #35327424, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 8513);