Finite Group Databasebeta

← Prev (#17987662) Next (#17987664) →

D5×C11⋊AGL(1,𝔽7) #17987663

order4620
automorphism?
homologyAbelianization (H1) = C22×C3 · Schur multiplier (H2) = C2

Aliases

direct productD5×C11⋊AGL(1,𝔽7)
unambiguous semidirect product(D5×C11)⋊AGL(1,𝔽7)
unambiguous semidirect product(D5×ΓL(1,𝔽8))⋊D11
unambiguous semidirect product(D5×D77)⋊C3

Splittings

Fitting, socle, derived, HallC5×C7×C11 ⋊ C22×C3
HallD5×D77 ⋊ C3
HallC5×C11×ΓL(1,𝔽8) ⋊ C22
HallC11×ΓL(1,𝔽8) ⋊ C2×D5
HallC5×ΓL(1,𝔽8) ⋊ C2×D11
HallC7×C11 ⋊ C2×C3×D5
HallC5×C11 ⋊ C2×AGL(1,𝔽7)
HallC5×C7 ⋊ C2×C3×D11
HallΓL(1,𝔽8) ⋊ D5×D11
SylowC11 ⋊ D5×AGL(1,𝔽7)
SylowC7 ⋊ C3×D5×D11
SylowC5 ⋊ C2×C11⋊AGL(1,𝔽7)

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC5×C7×C11C22×C3
LCSG ▷ C5×C7×C11
UCSC1

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 23
transitive degreeμt(G) = 385

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×D5×C11⋊AGL(1,𝔽7), D15×C11⋊AGL(1,𝔽7), D5×C3⋊(C11⋊AGL(1,𝔽7)), …
maximal normal subgroup ofC3×D5×C11⋊AGL(1,𝔽7), D5×ΓL(1,𝔽8)⋊AGL(1,𝔽11), C5×D5×C11⋊AGL(1,𝔽7), …
maximal quotient ofD5×C11⋊(D7⋊C9), C3×D5×C11⋊AGL(1,𝔽7), D15×C11⋊AGL(1,𝔽7), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4620, 60);