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C3×ΓL(1,𝔽8)×D95 #26046178

order11970
automorphism?
homologyAbelianization (H1) = C2×C32 · Schur multiplier (H2) = C3

Aliases

direct productC3×ΓL(1,𝔽8)×D95
unambiguous semidirect productC5⋊(C3×ΓL(1,𝔽8)×D19)

Splittings

Fitting, socleC3×C5×C7×C19 ⋊ C2×C3
derived, HallC5×C7×C19 ⋊ C2×C32
HallC3×C5×C19×ΓL(1,𝔽8) ⋊ C2
HallC7×D95 ⋊ C32
HallC3×C19×ΓL(1,𝔽8) ⋊ D5
HallC3×C5×ΓL(1,𝔽8) ⋊ D19
HallC7×C19 ⋊ C32×D5
HallC5×C19 ⋊ C2×C3×ΓL(1,𝔽8)
HallC5×C7 ⋊ C32×D19
SylowC19 ⋊ C3×D5×ΓL(1,𝔽8)
SylowC7 ⋊ C32×D95
SylowC5 ⋊ C3×ΓL(1,𝔽8)×D19

Subgroups

subgroupG/H
center, hypercenterC3ΓL(1,𝔽8)×D95
commutator, cosocle, hypocenterC5×C7×C19C2×C32
FrattiniC1G
Fitting, socleC3×C5×C7×C19C2×C3
LCSG ▷ C5×C7×C19
UCSC1 ◁ C3

96 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

735 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×AGL(1,𝔽7)×D95, C3×(C5⋊AGL(1,𝔽7))⋊D19, C3×D5×ΓL(1,𝔽8)×D19, …
maximal normal subgroup ofC3×AGL(1,𝔽7)×D95, C3×(C5⋊AGL(1,𝔽7))⋊D19, C3×D5×ΓL(1,𝔽8)×D19, …
maximal quotient ofC3×ΓL(1,𝔽8)×Dic95, C2×C3×ΓL(1,𝔽8)×D95

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11970, 107);