Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C27 |
| direct product | C2×#102×D83 |
| Fitting | C2×#102×C83 ⋊ C2 |
| Sylow | C83 ⋊ C22×#102 |
1072 conjugacy classes of subgroups.
1204 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C4×#102×D83, #1762×D83, #35402212, … |
| maximal normal subgroup of | C4×#102×D83, #1762×D83, #35402212, … |
| maximal quotient of | C2×D4⋊C8×D83, #1486×D83, C2×#24905886, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 12994);