Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C22×C4 |
| direct product | C4×C4⋊#3622 |
| Sylow | C17 ⋊ C4×C4⋊C8 |
316 conjugacy classes of subgroups; only the 213 normal subgroups are shown.
This group has 316 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) = 2176 |
592 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #16920851, #16920852, #16920866, … |
| maximal normal subgroup of | #16920851, #16920852, #16920866, … |
| maximal quotient of | C8×C4⋊#3622, #16925449, #16925458, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 4359);