Finite Group Databasebeta

← Prev (#87919) Next (#87921) →

Cayley diagram

C22×C5×AGL(1,𝔽5) #87920

order400
isoclinismisoclinic class of AGL(1,𝔽5)
automorphism?
homologyAbelianization (H1) = C22×C4×C5 · Schur multiplier (H2) = C23

Aliases

direct productC22×C5×AGL(1,𝔽5)
unambiguous semidirect productD5⋊(C2×C4×C5)

Splittings

Fitting, socleC22×C52 ⋊ C4
derivedC5 ⋊ C22×C4×C5
SylowC52 ⋊ C22×C4

Subgroups

subgroupG/H
center, hypercenterC22×C5AGL(1,𝔽5)
commutator, hypocenterC5C22×C4×C5
FrattiniC1G
Fitting, socleC22×C52C4
prime radicalC22×C5×D5C2
cosocleD5C23×C5
LCSG ▷ C5
UCSC1 ◁ C22×C5

113 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 14
transitive degreeμt(G) = 80

A minimal faithful permutation representation — 3 generators on 14 points:

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

Conjugacy classes & character table

100 conjugacy classes — view the full character table.

Relationships

maximal subgroup of(C2×AGL(1,𝔽5))⋊Dic5, C5×(C2×AGL(1,𝔽5))⋊C4, C2×Dic5×AGL(1,𝔽5), …
maximal normal subgroup of(C2×AGL(1,𝔽5))⋊Dic5, C5×(C2×AGL(1,𝔽5))⋊C4, C2×Dic5×AGL(1,𝔽5), …
maximal quotient ofC2×C5×D5⋊C8, C2×C5×#700, C5×D5⋊M16, …
automorphism group ofC11×Dic5, C2×D5×C11, C3×D5×C11, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(400, 214);