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C67⋊AGL(1,𝔽5) #13050699

order1340
isoclinismisoclinic class of C67⋊AGL(1,𝔽5)
automorphism?
homologyAbelianization (H1) = C4 · Schur multiplier (H2) = C1

Aliases

unambiguous semidirect productC67⋊AGL(1,𝔽5)

Splittings

Fitting, socle, derived, HallC5×C67 ⋊ C4
SylowC67 ⋊ AGL(1,𝔽5)
SylowC5 ⋊ Dic67

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC5×C67C4
prime radical, cosocleD5×C67C2
LCSG ▷ C5×C67
UCSC1

12 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 72
transitive degreeμt(G) = 335

Polycyclic presentation:

2^2,5,67|a^2=b,c^a=c^2,d^a=d^66,c^b=c^4

Conjugacy classes & character table

137 conjugacy classes — view the full character table.

Relationships

maximal subgroup of(C67⋊C3)⋊AGL(1,𝔽5), C3×C67⋊AGL(1,𝔽5), C3⋊(C67⋊AGL(1,𝔽5)), …
maximal normal subgroup of(C67⋊C3)⋊AGL(1,𝔽5), C3×C67⋊AGL(1,𝔽5), (C67⋊C11)⋊AGL(1,𝔽5), …
maximal quotient ofC3×C67⋊AGL(1,𝔽5), C3⋊(C67⋊AGL(1,𝔽5)), C67⋊#4380, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1340, 6);