Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
| direct product | C2×#19128257 |
| Fitting | C2×#125×C83 ⋊ C2 |
| Sylow | C83 ⋊ C2×#533 |
1168 conjugacy classes of subgroups; only the 541 normal subgroups are shown.
This group has 1168 conjugacy classes of subgroups — too many to draw. Only its 541 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1204 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35295883, #35370417, #35370536, … |
| maximal normal subgroup of | #35295883, #35370417, #35370536, … |
| maximal quotient of | C2×#24909869, C2×#24909936, C2×#24909944, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 17800);