Finite Group Databasebeta

← Prev (#16813229) Next (#16813231) →

C179⋊AGL(1,𝔽5) #16813230

order3580
automorphism?
homologyAbelianization (H1) = C4 · Schur multiplier (H2) = C1

Aliases

unambiguous semidirect productC179⋊AGL(1,𝔽5)

Splittings

Fitting, socle, derived, HallC5×C179 ⋊ C4
SylowC179 ⋊ AGL(1,𝔽5)
SylowC5 ⋊ Dic179

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC5×C179C4
prime radical, cosocleD5×C179C2
LCSG ▷ C5×C179
UCSC1

12 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 184
transitive degreeμt(G) = 895

Polycyclic presentation:

2^2,5,179|a^2=b,c^a=c^2,d^a=d^178,c^b=c^4

Conjugacy classes & character table

361 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC179⋊#1035, C5×C179⋊AGL(1,𝔽5), C179⋊#1043, …
maximal normal subgroup ofC5×C179⋊AGL(1,𝔽5), C7×C179⋊AGL(1,𝔽5)
maximal quotient ofC179⋊#1035, C5×C179⋊AGL(1,𝔽5), C179⋊#1043, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3580, 7);