Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C29 |
| direct product | #568×D83 |
| Fitting | #568×C83 ⋊ C2 |
| Sylow | C83 ⋊ C2×#568 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C4 | C24×D83 |
| commutator, socle | C2×C83 | C24×C4 |
| Fitting | #568×C83 | C2 |
| prime radical | C2×#41×D83 | C2 |
| cosocle | C4×C83 | C25 |
| hypercenter | #568 | D83 |
| hypocenter | C83 | C2×#568 |
| LCS | G ▷ C2×C83 ▷ C83 | |
| UCS | C1 ◁ C4 ◁ #568 | |
1460 conjugacy classes of subgroups.
1462 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #1858×D83, #35405248, #1861×D83, … |
| maximal normal subgroup of | #1858×D83, #35405248, #1861×D83, … |
| maximal quotient of | #2873×D83, #2875×D83, #568×Dic83, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 19217);