Finite Group DatabasebetaFinite Group Databasebeta| order | 17094 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C11⋊((C37⋊C3)⋊D7) |
| unambiguous semidirect product | (C37⋊C3)⋊D77 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C7×C11×C37 | C2×C3 |
| LCS | G ▷ C7×C11×C37 | |
| UCS | C1 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2849 |
Polycyclic presentation:
2,3,7,11,37|c^a=c^6,d^a=d^10,e^a=e^36,e^b=e^26582 conjugacy classes — view the full character table.
| maximal subgroup of | D77×D37⋊C3, D11×(C37⋊C3)⋊D7, D7×C11⋊(D37⋊C3), … |
| maximal normal subgroup of | D77×D37⋊C3, D11×(C37⋊C3)⋊D7, D7×C11⋊(D37⋊C3), … |
| maximal quotient of | C11⋊#15690918, C2×C11⋊((C37⋊C3)⋊D7) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17094, 45);