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C5×ΓL(1,𝔽8)×D67 #28380950

order14070
automorphism?
homologyAbelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×ΓL(1,𝔽8)×D67

Splittings

Fitting, socle, HallC5×C7×C67 ⋊ C2×C3
derived, HallC7×C67 ⋊ C2×C3×C5
HallC5×ΓL(1,𝔽8)×C67 ⋊ C2
HallC5×C7×D67 ⋊ C3
HallΓL(1,𝔽8)×C67 ⋊ C2×C5
HallC7×D67 ⋊ C3×C5
HallC5×C67 ⋊ C2×ΓL(1,𝔽8)
SylowC67 ⋊ C2×C5×ΓL(1,𝔽8)
HallC5×C7 ⋊ C3×D67
SylowC7 ⋊ C3×C5×D67

Subgroups

subgroupG/H
center, hypercenterC5ΓL(1,𝔽8)×D67
commutator, cosocle, hypocenterC7×C67C2×C3×C5
FrattiniC1G
Fitting, socleC5×C7×C67C2×C3
LCSG ▷ C7×C67
UCSC1 ◁ C5

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2345

Conjugacy classes & character table

875 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC5×AGL(1,𝔽7)×D67, D67×C5⋊AGL(1,𝔽7), D5×ΓL(1,𝔽8)×D67, …
maximal normal subgroup ofC5×AGL(1,𝔽7)×D67, D67×C5⋊AGL(1,𝔽7), D5×ΓL(1,𝔽8)×D67, …
maximal quotient ofC5×ΓL(1,𝔽8)×Dic67, C2×C5×ΓL(1,𝔽8)×D67

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14070, 22);