Finite Group DatabasebetaFinite Group Databasebeta| order | 2192 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C2×C4×C137 ⋊ C2 |
| Sylow | C137 ⋊ C22⋊C4 |
34 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1096 |
Polycyclic presentation:
2^4,137|a^2=d,b^a=bc,e^b=e^136554 conjugacy classes — view the full character table.
| maximal subgroup of | C22⋊C4×D137, C2×#14555487, #17984045, … |
| maximal normal subgroup of | C22⋊C4×D137, C2×#14555487, #17984045, … |
| maximal quotient of | #17983995, #17984000, #17984002, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2192, 17);