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(C5⋊AGL(1,𝔽7))⋊D5 #14523601

order2100
isoclinismisoclinic class of (C5⋊AGL(1,𝔽7))⋊D5
automorphism?
homologyAbelianization (H1) = C22×C3 · Schur multiplier (H2) = C2

Aliases

unambiguous semidirect product(C5⋊AGL(1,𝔽7))⋊D5
unambiguous semidirect product((C5⋊D5)⋊D7)⋊C3

Splittings

Fitting, socle, derived, HallC52×C7 ⋊ C22×C3
Hall(C5⋊D5)⋊D7 ⋊ C3
HallC52×ΓL(1,𝔽8) ⋊ C22
SylowC52 ⋊ C2×AGL(1,𝔽7)
HallΓL(1,𝔽8) ⋊ D52
SylowC7 ⋊ C3×D52

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC52×C7C22×C3
LCSG ▷ C52×C7
UCSC1

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 70

Polycyclic presentation:

2^2,3,5^2,7|d^a=d^4,f^a=f^6,d^b=d^4,e^b=e^4,f^c=f^2

Conjugacy classes & character table

62 conjugacy classes — view the full character table.

Relationships

maximal subgroup of(C5⋊(D49⋊C3))⋊D5, C7×(C5⋊AGL(1,𝔽7))⋊D5, #28413313, …
maximal normal subgroup ofC7×(C5⋊AGL(1,𝔽7))⋊D5, C11×(C5⋊AGL(1,𝔽7))⋊D5, C13×(C5⋊AGL(1,𝔽7))⋊D5, …
maximal quotient of(C5⋊(D49⋊C3))⋊D5, C7×(C5⋊AGL(1,𝔽7))⋊D5, #28413313, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2100, 81);