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C73×C7⋊AGL(1,𝔽5) #23779362

order10220
isoclinismisoclinic class of C7⋊AGL(1,𝔽5)
automorphism?
homologyAbelianization (H1) = C4×C73 · Schur multiplier (H2) = C1

Aliases

direct productC73×C7⋊AGL(1,𝔽5)
unambiguous semidirect productC7⋊(AGL(1,𝔽5)×C73)

Splittings

Fitting, socle, HallC5×C7×C73 ⋊ C4
derived, HallC5×C7 ⋊ C4×C73
HallC7×C73 ⋊ AGL(1,𝔽5)
HallC5×C73 ⋊ Dic7
SylowC7 ⋊ AGL(1,𝔽5)×C73
SylowC5 ⋊ Dic7×C73

Subgroups

subgroupG/H
center, hypercenterC73C7⋊AGL(1,𝔽5)
commutator, hypocenterC5×C7C4×C73
FrattiniC1G
Fitting, socleC5×C7×C73C4
prime radicalC7×D5×C73C2
cosocleC7×D5C2×C73
LCSG ▷ C5×C7
UCSC1 ◁ C73

24 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1241 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC73×ΓL(1,𝔽8)⋊AGL(1,𝔽5), #44501312, #44501313, …
maximal normal subgroup ofC73×ΓL(1,𝔽8)⋊AGL(1,𝔽5), #44501312, #44501313, …
maximal quotient ofC3×C73×C7⋊AGL(1,𝔽5), C73×C3⋊(C7⋊AGL(1,𝔽5))

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10220, 17);