Finite Group Databasebeta

C2×C4×C5⋊(C5⋊D5) #14522920

order2000
isoclinismisoclinic class of C5⋊(C5⋊D5)
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C23×C53

Aliases

direct productC2×C4×C5⋊(C5⋊D5)

Splittings

FittingC2×C4×C53 ⋊ C2
derived, SylowC53 ⋊ C22×C4

Subgroups

subgroupG/H
center, hypercenterC2×C4C5⋊(C5⋊D5)
commutator, hypocenterC53C22×C4
FrattiniC2C22×C5⋊(C5⋊D5)
FittingC2×C4×C53C2
socleC22×C53C22
prime radicalC22×C5⋊(C5⋊D5)C2
cosocleC2×C53C23
LCSG ▷ C53
UCSC1 ◁ C2×C4

1728 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1000

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2000, 883);