Finite Group DatabasebetaFinite Group Databasebeta| order | 4508 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C7 · Schur multiplier (H2) = C2 |
| direct product | C7×D7×D23 |
| unambiguous semidirect product | (D7×C23)⋊(C2×C7) |
| unambiguous semidirect product | (C7×D23)⋊(C2×C7) |
| unambiguous semidirect product | D161⋊(C2×C7) |
| Fitting, socle, Hall | C72×C23 ⋊ C22 |
| derived | C7×C23 ⋊ C22×C7 |
| Sylow | C72 ⋊ C2×D23 |
| Sylow | C23 ⋊ C2×C7×D7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | D7×D23 |
| commutator, cosocle, hypocenter | C7×C23 | C22×C7 |
| Frattini | C1 | G |
| Fitting, socle | C72×C23 | C22 |
| LCS | G ▷ C7×C23 | |
| UCS | C1 ◁ C7 | |
52 conjugacy classes of subgroups.
| transitive degree | μt(G) = 322 |
455 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C7×AGL(1,𝔽7)×D23, D23×#64423, D23×#64422, … |
| maximal normal subgroup of | C7×AGL(1,𝔽7)×D23, D23×#64423, D23×#64422, … |
| maximal quotient of | C3×C7×D7×D23, C7×D21×D23, C7×D7×D69, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4508, 17);