Finite Group DatabasebetaFinite Group Databasebeta| order | 2368 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C37 ⋊ #389 |
170 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 170 conjugacy classes of subgroups — too many to draw. Only its 77 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 2368 |
Polycyclic presentation:
2^6,37|a^2=f,b^2=f,c^2=e,b^a=bd,c^a=ce,g^c=g^36388 conjugacy classes — view the full character table.
| maximal subgroup of | #389×D37, C2×#14557428, #17997055, … |
| maximal normal subgroup of | #389×D37, C2×#14557428, #17997055, … |
| maximal quotient of | #17992824, #17992828, #17992831, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2368, 444);