Finite Group DatabasebetaFinite Group Databasebeta| order | 2368 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C2×C22⋊C4×C37 ⋊ C2 |
| Sylow | C37 ⋊ #394 |
238 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 238 conjugacy classes of subgroups — too many to draw. Only its 61 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|c^2=d,b^a=bd,c^a=ce,c^b=cf,g^b=g^36382 conjugacy classes — view the full character table.
| maximal subgroup of | #394×D37, C2×#14557448, #17997810, … |
| maximal normal subgroup of | #394×D37, C2×#14557448, #17997810, … |
| maximal quotient of | #17992835, #17992839, #17992840, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2368, 464);