Finite Group DatabasebetaFinite Group Databasebeta| order | 2368 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | #104×C37 ⋊ C2 |
| Sylow | C37 ⋊ #444 |
104 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 104 conjugacy classes of subgroups — too many to draw. Only its 45 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 53 |
| transitive degree | μt(G) = 592 |
Polycyclic presentation:
2^6,37|a^2=e,c^2=e,d^2=f,e^2=f,b^a=bd,c^a=cf,d^a=df,d^b=df,g^c=g^36274 conjugacy classes — view the full character table.
| maximal subgroup of | #444×D37, C2×#14557652, #18003494, … |
| maximal normal subgroup of | #444×D37, C2×#14557652, #18003494, … |
| maximal quotient of | #17993405, #17993411, #17993412, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2368, 668);