Finite Group Databasebeta

← Prev (#92128) Next (#92130) →

Cayley diagram

C23×C3×AGL(1,𝔽5) #92129

order480
isoclinismisoclinic class of AGL(1,𝔽5)
automorphism?
homologyAbelianization (H1) = C23×C3×C4 · Schur multiplier (H2) = C26

Aliases

direct productC23×C3×AGL(1,𝔽5)
unambiguous semidirect productD5⋊(C22×C3×C4)

Splittings

Fitting, socleC23×C3×C5 ⋊ C4
derived, SylowC5 ⋊ C23×C3×C4
HallC3×C5 ⋊ C23×C4

Subgroups

subgroupG/H
center, hypercenterC23×C3AGL(1,𝔽5)
commutator, hypocenterC5C23×C3×C4
FrattiniC1G
Fitting, socleC23×C3×C5C4
prime radicalC23×C3×D5C2
cosocleD5C24×C3
LCSG ▷ C5
UCSC1 ◁ C23×C3

472 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 14
transitive degreeμt(G) = 120

A minimal faithful permutation representation — 4 generators on 14 points:

(7,8,9)(11,12,13,14);(5,6)(10,11,12,14,13);(3,4);(1,2)

Conjugacy classes & character table

120 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×(C2×AGL(1,𝔽5))⋊Dic3, AGL(1,𝔽5)×#217, #11752022, …
maximal normal subgroup ofC2×(C2×AGL(1,𝔽5))⋊Dic3, AGL(1,𝔽5)×#217, #11752022, …
maximal quotient ofC22×C3×D5⋊C8, C22×C3×#700, C2×C3×D5⋊M16, …
automorphism group ofC7×#168, C4×C7×D5, C7×C22⋊D5, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(480, 1205);