Finite Group DatabasebetaFinite Group Databasebeta| order | 18176 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C4 · Schur multiplier (H2) = C216 |
| direct product | C24×(C2×D71)⋊C4 |
| Fitting | C25×C4×C71 ⋊ C2 |
| Sylow | C71 ⋊ C24×C22⋊C4 |
43678 conjugacy classes of subgroups; only the 10859 normal subgroups are shown.
This group has 43678 conjugacy classes of subgroups — too many to draw. Only its 10859 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 9088 |
4640 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18176, 1076119);