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D5×ΓL(1,𝔽8)×D11 #17987665

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

Aliases

direct productD5×ΓL(1,𝔽8)×D11
unambiguous semidirect product(D5×C11)⋊(C2×ΓL(1,𝔽8))
unambiguous semidirect product(C5×D11)⋊(C2×ΓL(1,𝔽8))
unambiguous semidirect productD55⋊(C2×ΓL(1,𝔽8))
unambiguous semidirect product(C7×D5×D11)⋊C3

Splittings

Fitting, socle, derived, HallC5×C7×C11 ⋊ C22×C3
HallC7×D5×D11 ⋊ 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 ⋊ C22×ΓL(1,𝔽8)
HallC5×C7 ⋊ C2×C3×D11
SylowC11 ⋊ C2×D5×ΓL(1,𝔽8)
SylowC7 ⋊ C3×D5×D11
SylowC5 ⋊ C2×ΓL(1,𝔽8)×D11

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

140 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×D5×ΓL(1,𝔽8)×D11, ΓL(1,𝔽8)×D11×D15, D5×ΓL(1,𝔽8)×D33, …
maximal normal subgroup ofC3×D5×ΓL(1,𝔽8)×D11, D5×ΓL(1,𝔽8)×AGL(1,𝔽11), C5×D5×ΓL(1,𝔽8)×D11, …
maximal quotient ofD5×D11×C7⋊C9, C3×D5×ΓL(1,𝔽8)×D11, ΓL(1,𝔽8)×D11×D15, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4620, 62);