Finite Group DatabasebetaFinite Group Databasebeta| order | 17661 |
| automorphism | ? |
| homology | Abelianization (H1) = C3 · Schur multiplier (H2) = C29 |
| unambiguous semidirect product | C7⋊(C292⋊C3) |
| unambiguous semidirect product | C292⋊ΓL(1,𝔽8) |
| Fitting, socle, derived, Hall | C7×C292 ⋊ C3 |
| Sylow | C292 ⋊ ΓL(1,𝔽8) |
| Sylow | C7 ⋊ C292⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C7×C292 | C3 |
| LCS | G ▷ C7×C292 | |
| UCS | C1 | |
28 conjugacy classes of subgroups.
| transitive degree | μt(G) = 609 |
Polycyclic presentation:
3,7,29^2|b^a=b^2,c^a=c^11d^10,d^a=c^7d^171965 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D7⋊(C292⋊C3), #47977358, (C29⋊D29)⋊ΓL(1,𝔽8), … |
| maximal normal subgroup of | D7⋊(C292⋊C3), #47977358, (C29⋊D29)⋊ΓL(1,𝔽8), … |
| maximal quotient of | C2×C7⋊(C292⋊C3) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17661, 11);