Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C16 · Schur multiplier (H2) = C23 |
| direct product | C16×C22⋊D83 |
| Fitting | C22×C16×C83 ⋊ C2 |
| Sylow | C83 ⋊ D4×C16 |
174 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 174 conjugacy classes of subgroups — too many to draw. Only its 81 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
2704 conjugacy classes. The character table is too large to display.
| maximal subgroup of | (C22⋊D83)⋊C32, C32×C22⋊D83, #35324953, … |
| maximal normal subgroup of | (C22⋊D83)⋊C32, C32×C22⋊D83, #35324953, … |
| maximal quotient of | C16×#13050575, C16×#13050578, C16×#13050577, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 6328);