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C121⋊AGL(1,𝔽5) #14559043

order2420
isoclinismisoclinic class of C121⋊AGL(1,𝔽5)
automorphism?
homologyAbelianization (H1) = C4 · Schur multiplier (H2) = C1

Aliases

unambiguous semidirect productC121⋊AGL(1,𝔽5)

Splittings

Fitting, derived, HallC5×C121 ⋊ C4
SylowC121 ⋊ AGL(1,𝔽5)
SylowC5 ⋊ Dic121

Subgroups

subgroupG/H
center, hypercenterC1G
commutator, Fitting, hypocenterC5×C121C4
FrattiniC11C11⋊AGL(1,𝔽5)
socleC5×C11Dic11
prime radicalD5×C11D11
cosocleD5×C121C2
LCSG ▷ C5×C121
UCSC1

18 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 126
transitive degreeμt(G) = 605

Polycyclic presentation:

2^2,5,11^2|a^2=b,d^11=e^10,c^a=c^3,d^a=d^10e,e^a=e^10,c^b=c^4

Conjugacy classes & character table

245 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC121⋊#1035, (C121⋊C5)⋊AGL(1,𝔽5), C5×C121⋊AGL(1,𝔽5), …
maximal normal subgroup of(C121⋊C5)⋊AGL(1,𝔽5), C5×C121⋊AGL(1,𝔽5), C7×C121⋊AGL(1,𝔽5), …
maximal quotient ofC121⋊#1035, C5×C121⋊AGL(1,𝔽5), C121⋊#1043, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2420, 11);