Finite Group DatabasebetaFinite Group Databasebeta| order | 2368 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C22⋊C8×C37 ⋊ C2 |
| Sylow | C37 ⋊ #436 |
122 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 122 conjugacy classes of subgroups — too many to draw. Only its 51 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1184 |
Polycyclic presentation:
2^6,37|a^2=e,c^2=e,e^2=f,b^a=bd,c^a=cf,c^b=cf,g^c=g^36388 conjugacy classes — view the full character table.
| maximal subgroup of | #436×D37, C2×#14557608, #18003294, … |
| maximal normal subgroup of | #436×D37, C2×#14557608, #18003294, … |
| maximal quotient of | #17993478, #17993483, #17993489, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2368, 624);