Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C16 · Schur multiplier (H2) = C22 |
| direct product | C2×#19127534 |
| Fitting | C2×C32×C83 ⋊ C2 |
| Sylow | C83 ⋊ C2×M64 |
112 conjugacy classes of subgroups.
2704 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35292214, C4×#19127534, #35324580, … |
| maximal normal subgroup of | #35292214, C4×#19127534, #35324580, … |
| maximal quotient of | C2×#24905596, C4×#19127534, C2×(C2×D83)⋊C32, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 6801);