Finite Group DatabasebetaFinite Group Databasebeta| order | 2368 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C4⋊C8×C37 ⋊ C2 |
| Sylow | C37 ⋊ #424 |
114 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 114 conjugacy classes of subgroups — too many to draw. Only its 55 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,b^2=d,e^2=f,b^a=bd,c^b=cf,g^c=g^36388 conjugacy classes — view the full character table.
| maximal subgroup of | #424×D37, C2×#14557558, #18003157, … |
| maximal normal subgroup of | #424×D37, C2×#14557558, #18003157, … |
| maximal quotient of | #17993365, #17993369, #17993373, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2368, 574);