Finite Group DatabasebetaFinite Group Databasebeta| order | 2368 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| unambiguous semidirect product | D37⋊#131 |
| Sylow | C37 ⋊ C2×#131 |
266 conjugacy classes of subgroups.
| transitive degree | μt(G) = 592 |
Polycyclic presentation:
2^6,37|a^2=e,e^2=f,g^a=g^31,c^b=cf,g^d=g^36,g^e=g^36130 conjugacy classes — view the full character table.
| maximal subgroup of | #18010372, #18010376, #18010635, … |
| maximal normal subgroup of | #18010372, #18010376, #18010635, … |
| maximal quotient of | #18011156, C4×#11924623, C4×#11924624, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2368, 1625);