Finite Group DatabasebetaFinite Group Databasebeta| order | 2368 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C37 ⋊ #431 |
118 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1184 |
Polycyclic presentation:
2^6,37|a^2=e,c^2=d,e^2=f,b^a=bd,g^a=g^31,g^b=g^36,g^c=g^36,g^e=g^36184 conjugacy classes — view the full character table.
| maximal subgroup of | #18009423, #18009428, #18009451, … |
| maximal normal subgroup of | #18009423, #18009428, #18009451, … |
| maximal quotient of | #18010311, C4×#11924593, C4×C4⋊#64438, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2368, 1568);