Finite Group DatabasebetaFinite Group Databasebeta| order | 15918 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C7 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | (D379⋊C3)⋊C7 |
| unambiguous semidirect product | (D379⋊C7)⋊C3 |
| unambiguous semidirect product | ((C379⋊C3)⋊C7)⋊C2 |
| Fitting, socle, derived, Sylow | C379 ⋊ C2×C3×C7 |
| Hall | (C379⋊C3)⋊C7 ⋊ C2 |
| Hall | D379⋊C7 ⋊ C3 |
| Hall | C379⋊C7 ⋊ C2×C3 |
| Hall | D379⋊C3 ⋊ C7 |
| Hall | C379⋊C3 ⋊ C2×C7 |
| Hall | D379 ⋊ C3×C7 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C379 | C2×C3×C7 |
| LCS | G ▷ C379 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 379 |
Polycyclic presentation:
2,3,7,379|d^a=d^378,d^b=d^327,d^c=d^12551 conjugacy classes — view the full character table.
| maximal subgroup of | C2×(D379⋊C3)⋊C7 |
| maximal normal subgroup of | C2×(D379⋊C3)⋊C7 |
| maximal quotient of | ((C379⋊C3)⋊C4)⋊C7, C2×(D379⋊C3)⋊C7 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15918, 30);