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C67×C7⋊AGL(1,𝔽5) #22627738

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

Aliases

direct productC67×C7⋊AGL(1,𝔽5)
unambiguous semidirect productC7⋊(AGL(1,𝔽5)×C67)

Splittings

Fitting, socle, HallC5×C7×C67 ⋊ C4
derived, HallC5×C7 ⋊ C4×C67
HallC7×C67 ⋊ AGL(1,𝔽5)
HallC5×C67 ⋊ Dic7
SylowC7 ⋊ AGL(1,𝔽5)×C67
SylowC5 ⋊ Dic7×C67

Subgroups

subgroupG/H
center, hypercenterC67C7⋊AGL(1,𝔽5)
commutator, hypocenterC5×C7C4×C67
FrattiniC1G
Fitting, socleC5×C7×C67C4
LCSG ▷ C5×C7
UCSC1 ◁ C67

24 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1139 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC67×ΓL(1,𝔽8)⋊AGL(1,𝔽5), #43244883, #43244884, …
maximal normal subgroup ofC67×ΓL(1,𝔽8)⋊AGL(1,𝔽5), #43244883, #43244884, …
maximal quotient ofC3×C67×C7⋊AGL(1,𝔽5), C67×C3⋊(C7⋊AGL(1,𝔽5))

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9380, 13);