Finite Group DatabasebetaFinite Group Databasebeta| order | 1000 |
| isoclinism | isoclinic class of D53 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
| direct product | D53 |
| unambiguous semidirect product | (D5×C5⋊D5)⋊C2 |
| Fitting, socle, derived, Sylow | C53 ⋊ C23 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C53 | C23 |
| LCS | G ▷ C53 | |
| UCS | C1 | |
204 conjugacy classes of subgroups.
| transitive degree | μt(G) = 20 |
64 conjugacy classes — view the full character table.
| maximal subgroup of | #14522942, D5⋊(D5⋊AGL(1,𝔽5)), D5×D5⋊AGL(1,𝔽5), … |
| maximal normal subgroup of | #14522942, D5⋊(D5⋊AGL(1,𝔽5)), D5×D5⋊AGL(1,𝔽5), … |
| maximal quotient of | D52×Dic5, D5×#6036, #14522764, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1000, 183);