Finite Group DatabasebetaFinite Group Databasebeta| order | 2368 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C4×C8×C37 ⋊ C2 |
| Sylow | C37 ⋊ D4⋊C8 |
82 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1184 |
Polycyclic presentation:
2^6,37|a^2=d,c^2=e,d^2=f,b^a=bc,c^a=ce,g^a=g^36,c^b=ce,g^b=g^36604 conjugacy classes — view the full character table.
| maximal subgroup of | D4⋊C8×D37, C2×#14557262, #17992977, … |
| maximal normal subgroup of | D4⋊C8×D37, C2×#14557262, #17992977, … |
| maximal quotient of | #17992416, #17992418, #17992436, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2368, 278);