Finite Group DatabasebetaFinite Group Databasebeta| order | 4508 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D7×D161 |
| unambiguous semidirect product | (C7×D7)⋊D23 |
| unambiguous semidirect product | (D7×C23)⋊D7 |
| Fitting, socle, derived, Hall | C72×C23 ⋊ C22 |
| Sylow | C72 ⋊ C2×D23 |
| Sylow | C23 ⋊ D72 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C72×C23 | C22 |
| LCS | G ▷ C72×C23 | |
| UCS | C1 | |
52 conjugacy classes of subgroups.
| transitive degree | μt(G) = 322 |
410 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #64423⋊D23, #64422⋊D23, AGL(1,𝔽7)×D161, … |
| maximal normal subgroup of | #64423⋊D23, #64422⋊D23, AGL(1,𝔽7)×D161, … |
| maximal quotient of | C3×D7×D161, D7×D483, D21×D161, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4508, 20);