Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C27 |
| direct product | C2×#11762720 |
| Fitting | C23×Q8×C17 ⋊ C2 |
| Sylow | C17 ⋊ C2×#393 |
1036 conjugacy classes of subgroups; only the 269 normal subgroups are shown.
This group has 1036 conjugacy classes of subgroups — too many to draw. Only its 269 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1088 |
364 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #16929310, #16929325, #16934531, … |
| maximal normal subgroup of | #16929310, #16929325, #16934531, … |
| maximal quotient of | C2×#14527026, C2×#14527043, C2×#14527055, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 7709);