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C3×AGL(1,𝔽5)×C167 #23756608

order10020
isoclinismisoclinic class of AGL(1,𝔽5)
automorphism?
homologyAbelianization (H1) = C3×C4×C167 · Schur multiplier (H2) = C1

Aliases

direct productC3×AGL(1,𝔽5)×C167

Splittings

Fitting, socle, HallC3×C5×C167 ⋊ C4
derived, SylowC5 ⋊ C3×C4×C167
HallC5×C167 ⋊ C3×C4
HallC3×C5 ⋊ C4×C167

Subgroups

subgroupG/H
center, hypercenterC3×C167AGL(1,𝔽5)
commutator, hypocenterC5C3×C4×C167
FrattiniC1G
Fitting, socleC3×C5×C167C4
prime radicalC3×D5×C167C2
cosocleD5C2×C3×C167
LCSG ▷ C5
UCSC1 ◁ C3×C167

24 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2505 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC9×AGL(1,𝔽5)×C167, C32×AGL(1,𝔽5)×C167, C3×ΓL(1,𝔽16)×C167
maximal normal subgroup ofC9×AGL(1,𝔽5)×C167, C32×AGL(1,𝔽5)×C167
maximal quotient ofC9×AGL(1,𝔽5)×C167, C32×AGL(1,𝔽5)×C167, C3×ΓL(1,𝔽16)×C167

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10020, 10);