Finite Group DatabasebetaFinite Group Databasebeta| order | 6154 |
| automorphism | Aut(G) order 8861760 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D3077 |
| unambiguous semidirect product | C17⋊D181 |
| unambiguous semidirect product | C181⋊D17 |
| Fitting, socle, derived, Hall | C17×C181 ⋊ C2 |
| Sylow | C181 ⋊ D17 |
| Sylow | C17 ⋊ D181 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C17×C181 | C2 |
| LCS | G ▷ C17×C181 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
Polycyclic presentation:
2,17,181|b^a=b^16,c^a=c^1801540 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #27134417, #27134418, D17×D181, … |
| maximal normal subgroup of | #27134417, #27134418, D17×D181, … |
| maximal quotient of | Dic3077, C2×D3077, C3×D3077, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6154, 3);