Finite Group DatabasebetaFinite Group Databasebeta| order | 1808 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C113 ⋊ M16 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C2×#90673 |
| commutator, socle | C2×C113 | C2×C4 |
| Fitting, prime radical | C22×C113 | C4 |
| cosocle | Dic113 | C22 |
| hypercenter | C22 | #90673 |
| hypocenter | C113 | M16 |
| LCS | G ▷ C2×C113 ▷ C113 | |
| UCS | C1 ◁ C2 ◁ C22 | |
20 conjugacy classes of subgroups.
| transitive degree | μt(G) = 904 |
Polycyclic presentation:
2^4,113|a^2=c,c^2=d,b^a=bd,e^a=e^98,e^c=e^112122 conjugacy classes — view the full character table.
| maximal subgroup of | #16813682, #16813683, C2×#14268656, … |
| maximal normal subgroup of | #16813682, #16813683, C2×#14268656, … |
| maximal quotient of | #16813677, C22⋊#11744753, #16813689, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1808, 49);