Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| isoclinism | isoclinic class of D83 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C82 · Schur multiplier (H2) = C22×C8 |
| direct product | C82×D83 |
| Fitting | C82×C83 ⋊ C2 |
| derived, Sylow | C83 ⋊ C2×C82 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C82 | D83 |
| commutator, hypocenter | C83 | C2×C82 |
| Frattini | C42 | C22×D83 |
| Fitting | C82×C83 | C2 |
| socle | C22×C83 | C2×C42 |
| prime radical | C22×D83 | C42 |
| cosocle | C42×C83 | C23 |
| LCS | G ▷ C83 | |
| UCS | C1 ◁ C82 | |
280 conjugacy classes of subgroups.
2752 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C8×C16×D83, #1311×D83, C8×#14581731, … |
| maximal normal subgroup of | C8×C16×D83, #1311×D83, C8×#14581731, … |
| maximal quotient of | C82×Dic83, #1273×D83, #35294826, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 2782);