Finite Group DatabasebetaFinite Group Databasebeta| order | 2368 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | AGL(1,ℤ/8)×C37 ⋊ C2 |
| Sylow | C37 ⋊ #577 |
258 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 99 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 592 |
Polycyclic presentation:
2^6,37|a^2=f,e^2=f,b^a=be,e^a=ef,e^b=ef,g^b=g^36,d^c=df,g^c=g^36,g^d=g^36220 conjugacy classes — view the full character table.
| maximal subgroup of | #18006357, #18006359, #18006368, … |
| maximal normal subgroup of | #18006357, #18006359, #18006368, … |
| maximal quotient of | #18003121, #18003127, #18003190, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2368, 1359);