Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C25 |
| direct product | #41×#3633 |
| Fitting | #41×C17 ⋊ C8 |
| Sylow | C17 ⋊ C8×#41 |
456 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 197 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 136 |
100 conjugacy classes — view the full character table.
| maximal subgroup of | #104×#3633, #17981616, #17981730, … |
| maximal normal subgroup of | #104×#3633, #17981616, #17981730, … |
| maximal quotient of | #117×#3633, C4×D4×#3633, C4×Q8×#3633, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 21751);