Finite Group DatabasebetaFinite Group Databasebeta| order | 1808 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | C4⋊#90673 |
| Fitting | C4×C113 ⋊ C4 |
| Sylow | C113 ⋊ C4⋊C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C2×#90673 |
| commutator, socle | C2×C113 | C2×C4 |
| Fitting | C4×C113 | C4 |
| prime radical, cosocle | C2×D113 | C22 |
| hypercenter | C4 | #90673 |
| hypocenter | C113 | C4⋊C4 |
| LCS | G ▷ C2×C113 ▷ C113 | |
| UCS | C1 ◁ C2 ◁ C4 | |
26 conjugacy classes of subgroups.
| transitive degree | μt(G) = 452 |
Polycyclic presentation:
2^4,113|a^2=d,b^2=c,b^a=bc,e^a=e^98,e^d=e^112122 conjugacy classes — view the full character table.
| maximal subgroup of | #16813684, #16813685, #16813690, … |
| maximal normal subgroup of | #16813684, #16813685, #16813690, … |
| maximal quotient of | (C2×#90673)⋊C4, C4⋊#11744753, #16813689, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1808, 46);