Finite Group Databasebeta

← Prev (#13096821) Next (#13096823) →

C79⋊AGL(1,𝔽5) #13096822

order1580
isoclinismisoclinic class of C79⋊AGL(1,𝔽5)
automorphism?
homologyAbelianization (H1) = C4 · Schur multiplier (H2) = C1

Aliases

unambiguous semidirect productC79⋊AGL(1,𝔽5)

Splittings

Fitting, socle, derived, HallC5×C79 ⋊ C4
SylowC79 ⋊ AGL(1,𝔽5)
SylowC5 ⋊ Dic79

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC5×C79C4
prime radical, cosocleD5×C79C2
LCSG ▷ C5×C79
UCSC1

12 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 84
transitive degreeμt(G) = 395

Polycyclic presentation:

2^2,5,79|a^2=b,c^a=c^2,d^a=d^78,c^b=c^4

Conjugacy classes & character table

161 conjugacy classes — view the full character table.

Relationships

maximal subgroup of(C79⋊C3)⋊AGL(1,𝔽5), C3×C79⋊AGL(1,𝔽5), C3⋊(C79⋊AGL(1,𝔽5)), …
maximal normal subgroup of(C79⋊C3)⋊AGL(1,𝔽5), C3×C79⋊AGL(1,𝔽5), C7×C79⋊AGL(1,𝔽5), …
maximal quotient ofC3×C79⋊AGL(1,𝔽5), C3⋊(C79⋊AGL(1,𝔽5)), C7×C79⋊AGL(1,𝔽5), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1580, 6);