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C7×AGL(1,𝔽5)×C73 #23779358

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

Aliases

direct productC7×AGL(1,𝔽5)×C73

Splittings

Fitting, socle, HallC5×C7×C73 ⋊ C4
derived, SylowC5 ⋊ C4×C7×C73
HallC5×C73 ⋊ C4×C7
HallC5×C7 ⋊ C4×C73

Subgroups

subgroupG/H
center, hypercenterC7×C73AGL(1,𝔽5)
commutator, hypocenterC5C4×C7×C73
FrattiniC1G
Fitting, socleC5×C7×C73C4
prime radicalC7×D5×C73C2
cosocleD5C2×C7×C73
LCSG ▷ C5
UCSC1 ◁ C7×C73

24 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2555 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC7×AGL(1,𝔽5)×C73⋊C3, AGL(1,𝔽5)×ΓL(1,𝔽8)×C73, AGL(1,𝔽5)×#13095275, …
maximal normal subgroup ofC7×AGL(1,𝔽5)×C73⋊C3, AGL(1,𝔽5)×ΓL(1,𝔽8)×C73, AGL(1,𝔽5)×#13095275, …
maximal quotient ofC3×C7×AGL(1,𝔽5)×C73, C7×ΓL(1,𝔽16)×C73

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10220, 13);