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C7×D5⋊AGL(1,𝔽5) #13063830

order1400
isoclinismisoclinic class of D5⋊AGL(1,𝔽5)
automorphism?
homologyAbelianization (H1) = C2×C4×C7 · Schur multiplier (H2) = C2

Aliases

direct productC7×D5⋊AGL(1,𝔽5)
unambiguous semidirect productD5⋊(C7×AGL(1,𝔽5))
unambiguous semidirect product#1043⋊(C2×C7)

Splittings

Fitting, socle, HallC52×C7 ⋊ C2×C4
derived, SylowC52 ⋊ C2×C4×C7

Subgroups

subgroupG/H
center, hypercenterC7D5⋊AGL(1,𝔽5)
commutator, hypocenterC52C2×C4×C7
FrattiniC1G
Fitting, socleC52×C7C2×C4
prime radicalC7×D52C2
cosocleC5⋊D5C22×C7
LCSG ▷ C52
UCSC1 ◁ C7

76 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 17
transitive degreeμt(G) = 70

A minimal faithful permutation representation — 2 generators on 17 points:

(1,2,3,4,5,6,7)(8,17,13,14,10,12,11,16,15,9);(10,13,11,15)(12,16,14,17)

Conjugacy classes & character table

98 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofΓL(1,𝔽8)×D5⋊AGL(1,𝔽5), D7×D5⋊AGL(1,𝔽5), C7×#1043⋊D7, …
maximal normal subgroup ofΓL(1,𝔽8)×D5⋊AGL(1,𝔽5), D7×D5⋊AGL(1,𝔽5), C2×C7×D5⋊AGL(1,𝔽5), …
maximal quotient ofC7×#1043⋊D7, C7×#87830, C2×C7×D5⋊AGL(1,𝔽5), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1400, 119);