Finite Group DatabasebetaFinite Group Databasebeta| order | 1200 |
| isoclinism | isoclinic class of ((D5⋊AGL(1,𝔽5))⋊C2)⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | ((D5⋊AGL(1,𝔽5))⋊C2)⋊C3 |
| unambiguous semidirect product | (#6057⋊C3)⋊C2 |
| Fitting, socle, Sylow | C52 ⋊ #41⋊C3 |
| Hall | (D5⋊AGL(1,𝔽5))⋊C2 ⋊ C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | #6057 | C2×C3 |
| Fitting, socle | C52 | #41⋊C3 |
| LCS | G ▷ #6057 | |
| UCS | C1 | |
38 conjugacy classes of subgroups.
| minimal degree | μ(G) = 25 |
| transitive degree | μt(G) = 25 |
Polycyclic presentation:
2,3,2^3,5^2|a^2=e,c^2=e,d^2=e,f^a=f^2,g^a=g^2,c^b=cd,d^b=c,f^b=f^4g^3,g^b=f^3,d^c=de,f^c=fg,g^c=f^3g^4,f^d=f^2,g^d=fg^3,f^e=f^4,g^e=g^416 conjugacy classes — view the full character table.
| maximal subgroup of | #72210652, #72210663, C2×((D5⋊AGL(1,𝔽5))⋊C2)⋊C3 |
| maximal normal subgroup of | #72210663, C2×((D5⋊AGL(1,𝔽5))⋊C2)⋊C3 |
| maximal quotient of | C2×((D5⋊AGL(1,𝔽5))⋊C2)⋊C3, #72277859 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1200, 947);