Finite Group Databasebeta

← Prev (#13104446) Next (#13104448) →

C4×C5×C4⋊AGL(1,𝔽5) #13104447

order1600
isoclinismisoclinic class of #700
automorphism?
homologyAbelianization (H1) = C2×C42×C5 · Schur multiplier (H2) = C22×C4

Aliases

direct productC4×C5×C4⋊AGL(1,𝔽5)

Splittings

FittingC42×C52 ⋊ C4
SylowC52 ⋊ C4×C4⋊C4

Subgroups

subgroupG/H
centerC2×C4×C5C2×AGL(1,𝔽5)
commutatorC2×C5C2×C42×C5
FrattiniC22C22×C5×AGL(1,𝔽5)
FittingC42×C52C4
socleC22×C52C22×C4
prime radicalC22×C5×D5C23
cosocleC22×D5C23×C5
hypercenterC42×C5AGL(1,𝔽5)
hypocenterC5C4×C5×C4⋊C4
LCSG ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C4×C5 ◁ C42×C5

403 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 320

Conjugacy classes & character table

280 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1600, 6799);