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C5×ΓL(1,𝔽8)×D57 #26046194

order11970
automorphism?
homologyAbelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×ΓL(1,𝔽8)×D57
unambiguous semidirect productC3⋊(C5×ΓL(1,𝔽8)×D19)

Splittings

Fitting, socleC3×C5×C7×C19 ⋊ C2×C3
derivedC3×C7×C19 ⋊ C2×C3×C5
HallC3×C5×C19×ΓL(1,𝔽8) ⋊ C2
HallC3×C19×ΓL(1,𝔽8) ⋊ C2×C5
HallC5×C7×C19 ⋊ C3×D3
HallC3×C5×ΓL(1,𝔽8) ⋊ D19
HallC7×C19 ⋊ C3×C5×D3
HallC5×C19 ⋊ D3×ΓL(1,𝔽8)
HallC3×ΓL(1,𝔽8) ⋊ C5×D19
HallC5×C7 ⋊ C3×D57
SylowC19 ⋊ C5×D3×ΓL(1,𝔽8)
SylowC7 ⋊ C3×C5×D57

Subgroups

subgroupG/H
center, hypercenterC5ΓL(1,𝔽8)×D57
commutator, cosocle, hypocenterC3×C7×C19C2×C3×C5
FrattiniC1G
Fitting, socleC3×C5×C7×C19C2×C3
LCSG ▷ C3×C7×C19
UCSC1 ◁ C5

72 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

750 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC5×AGL(1,𝔽7)×D57, C5×(C3⋊AGL(1,𝔽7))⋊D19, C5×D3×ΓL(1,𝔽8)×D19, …
maximal normal subgroup ofC5×AGL(1,𝔽7)×D57, C5×(C3⋊AGL(1,𝔽7))⋊D19, C5×D3×ΓL(1,𝔽8)×D19, …
maximal quotient ofC5×ΓL(1,𝔽8)×Dic57, C2×C5×ΓL(1,𝔽8)×D57

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11970, 123);