Finite Group DatabasebetaFinite Group Databasebeta| order | 2368 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | C22⋊#10596925 |
| Sylow | C37 ⋊ C22⋊C16 |
66 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1184 |
Polycyclic presentation:
2^6,37|a^2=d,d^2=e,e^2=f,b^a=bc,g^a=g^36616 conjugacy classes — view the full character table.
| maximal subgroup of | #17992519, #17992520, #17992521, … |
| maximal normal subgroup of | #17992519, #17992520, #17992521, … |
| maximal quotient of | #17992520, #17992536, D4⋊#10596925, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2368, 329);