Finite Group DatabasebetaFinite Group Databasebeta| order | 2384 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | C22⋊#10597010 |
| unambiguous semidirect product | (C2×#10597010)⋊C2 |
| Fitting | C22×C149 ⋊ C4 |
| Sylow | C149 ⋊ C22⋊C4 |
34 conjugacy classes of subgroups.
| transitive degree | μt(G) = 596 |
Polycyclic presentation:
2^4,149|a^2=d,b^a=bc,e^a=e^105,e^d=e^148158 conjugacy classes — view the full character table.
| maximal subgroup of | #18011969, #18011970, C2×C22⋊#10597010, … |
| maximal normal subgroup of | #18011969, #18011970, C2×C22⋊#10597010, … |
| maximal quotient of | (C2×#10597010)⋊C4, C22⋊#11924753, #18011968, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2384, 45);