Finite Group DatabasebetaFinite Group Databasebeta| order | 1008 |
| isoclinism | isoclinic class of D7×#157 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C3×C4 |
| direct product | Dic7×#157 |
| derived, Hall | C32×C7 ⋊ C42 |
| Sylow | C32 ⋊ C4×Dic7 |
| Sylow | C7 ⋊ C4×#157 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D7×#157 |
| commutator, hypocenter | C32×C7 | C42 |
| Fitting, socle | C2×C32×C7 | C2×C4 |
| prime radical, cosocle | C2×C7×C3⋊D3 | C22 |
| LCS | G ▷ C32×C7 | |
| UCS | C1 ◁ C2 | |
92 conjugacy classes of subgroups.
| transitive degree | μt(G) = 168 |
60 conjugacy classes — view the full character table.
| maximal subgroup of | #157×C7⋊AGL(1,𝔽5), #157×ΓL(1,𝔽8)⋊C4, #72217264, … |
| maximal normal subgroup of | #157×ΓL(1,𝔽8)⋊C4, C4×D7×#157, Dic7×AGL(1,𝔽9), … |
| maximal quotient of | #157×C7⋊AGL(1,𝔽5), #72217264 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1008, 559);