Finite Group DatabasebetaFinite Group Databasebeta| order | 2368 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | C2×Q8×#3866 |
| unambiguous semidirect product | D37⋊(C4×Q8) |
| Fitting | C2×Q8×C37 ⋊ C4 |
| Sylow | C37 ⋊ C2×C4×Q8 |
298 conjugacy classes of subgroups.
| transitive degree | μt(G) = 592 |
130 conjugacy classes — view the full character table.
| maximal subgroup of | #101×#3866, #103×#3866, #18010369, … |
| maximal normal subgroup of | #101×#3866, #103×#3866, #18010369, … |
| maximal quotient of | C2×C4⋊C4×#3866, C4×Q8×#3866, C2×#14558482, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2368, 1614);