Finite Group Databasebeta

← Prev (#14268408) Next (#14268410) →

C32×D5⋊AGL(1,𝔽5) #14268409

order1800
isoclinismisoclinic class of D5⋊AGL(1,𝔽5)
automorphism?
homologyAbelianization (H1) = C2×C32×C4 · Schur multiplier (H2) = C2×C3

Aliases

direct productC32×D5⋊AGL(1,𝔽5)
unambiguous semidirect productD5⋊(C32×AGL(1,𝔽5))

Splittings

Fitting, socle, HallC32×C52 ⋊ C2×C4
derived, SylowC52 ⋊ C2×C32×C4

Subgroups

subgroupG/H
center, hypercenterC32D5⋊AGL(1,𝔽5)
commutator, hypocenterC52C2×C32×C4
FrattiniC1G
Fitting, socleC32×C52C2×C4
prime radicalC32×D52C2
cosocleC5⋊D5C22×C32
LCSG ▷ C52
UCSC1 ◁ C32

228 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 16
transitive degreeμt(G) = 90

A minimal faithful permutation representation — 2 generators on 16 points:

(1,2,3)(7,16,12,13,9,11,10,15,14,8);(4,5,6)(9,12,10,14)(11,15,13,16)

Conjugacy classes & character table

126 conjugacy classes — view the full character table.

Relationships

maximal subgroup of3−1+2×D5⋊AGL(1,𝔽5), C3×D3×D5⋊AGL(1,𝔽5), C32×#10597182, …
maximal normal subgroup of3−1+2×D5⋊AGL(1,𝔽5), C3×D3×D5⋊AGL(1,𝔽5), C3⋊D3×D5⋊AGL(1,𝔽5), …
maximal quotient of3−1+2×D5⋊AGL(1,𝔽5), C32×#10597182, C32×#87830, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1800, 603);