Finite Group DatabasebetaFinite Group Databasebeta| order | 17872 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
| direct product | C2×Dic2234 |
| unambiguous semidirect product | (C2×C1117)⋊Q8 |
| Sylow | C1117 ⋊ C2×Q8 |
38 conjugacy classes of subgroups.
| transitive degree | μt(G) = 17872 |
4474 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #49088450, #49088455, #49088457, … |
| maximal normal subgroup of | #49088450, #49088455, #49088457, … |
| maximal quotient of | C2×#31821889, C2×C4⋊Dic1117, C4×Dic2234, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17872, 38);