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(C43⋊C3)⋊AGL(1,𝔽5) #14579502

order2580
isoclinismisoclinic class of (C43⋊C3)⋊AGL(1,𝔽5)
automorphism?
homologyAbelianization (H1) = C3×C4 · Schur multiplier (H2) = C1

Aliases

unambiguous semidirect product(C43⋊C3)⋊AGL(1,𝔽5)
unambiguous semidirect product(C43⋊AGL(1,𝔽5))⋊C3

Splittings

Fitting, socle, derived, HallC5×C43 ⋊ C3×C4
HallC43⋊AGL(1,𝔽5) ⋊ C3
HallC5×C43⋊C3 ⋊ C4
HallC43⋊C3 ⋊ AGL(1,𝔽5)
SylowC43 ⋊ C3×AGL(1,𝔽5)
SylowC5 ⋊ (C43⋊C3)⋊C4

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC5×C43C3×C4
prime radicalD5×C43⋊C3C2
cosocleD5×C43C2×C3
LCSG ▷ C5×C43
UCSC1

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 48
transitive degreeμt(G) = 215

Polycyclic presentation:

2,3,2,5,43|a^2=c,d^a=d^2,e^a=e^42,e^b=e^36,d^c=d^4

Conjugacy classes & character table

43 conjugacy classes — view the full character table.

Relationships

maximal subgroup of(C43⋊C3)⋊#1035, C5×(C43⋊C3)⋊AGL(1,𝔽5), (C43⋊C3)⋊#1043, …
maximal normal subgroup ofC5×(C43⋊C3)⋊AGL(1,𝔽5), ((C43⋊C3)⋊C7)⋊AGL(1,𝔽5), C7×(C43⋊C3)⋊AGL(1,𝔽5), …
maximal quotient of(C43⋊C3)⋊#1035, C5×(C43⋊C3)⋊AGL(1,𝔽5), (C43⋊C3)⋊#1043, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2580, 14);