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C7×AGL(1,𝔽5)×C67 #22627736

order9380
isoclinismisoclinic class of AGL(1,𝔽5)
automorphism?
homologyAbelianization (H1) = C4×C7×C67 · Schur multiplier (H2) = C1

Aliases

direct productC7×AGL(1,𝔽5)×C67

Splittings

Fitting, socle, HallC5×C7×C67 ⋊ C4
derived, SylowC5 ⋊ C4×C7×C67
HallC5×C67 ⋊ C4×C7
HallC5×C7 ⋊ C4×C67

Subgroups

subgroupG/H
center, hypercenterC7×C67AGL(1,𝔽5)
commutator, hypocenterC5C4×C7×C67
FrattiniC1G
Fitting, socleC5×C7×C67C4
LCSG ▷ C5
UCSC1 ◁ C7×C67

24 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2345 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC7×AGL(1,𝔽5)×C67⋊C3, AGL(1,𝔽5)×ΓL(1,𝔽8)×C67, AGL(1,𝔽5)×#13064104, …
maximal normal subgroup ofC7×AGL(1,𝔽5)×C67⋊C3, AGL(1,𝔽5)×ΓL(1,𝔽8)×C67, AGL(1,𝔽5)×#13064104, …
maximal quotient ofC3×C7×AGL(1,𝔽5)×C67, C7×ΓL(1,𝔽16)×C67

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9380, 11);