Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C23×C4 |
| direct product | C4×C22⋊#3622 |
| Sylow | C17 ⋊ C4×C22⋊C8 |
436 conjugacy classes of subgroups; only the 213 normal subgroups are shown.
This group has 436 conjugacy classes of subgroups — too many to draw. Only its 213 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1088 |
592 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #16920853, #16920854, #16920863, … |
| maximal normal subgroup of | #16920853, #16920854, #16920863, … |
| maximal quotient of | C8×C22⋊#3622, #16924793, #16924802, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 4268);