Finite Group Databasebeta

C25×C22⋊Dic5 #14522212

order2000
isoclinismisoclinic class of Dic10
automorphism?
homologyAbelianization (H1) = C2×C4×C25 · Schur multiplier (H2) = C22

Aliases

direct productC25×C22⋊Dic5
unambiguous semidirect productC22⋊(Dic5×C25)

Splittings

SylowC5×C25 ⋊ C22⋊C4

Subgroups

subgroupG/H
centerC22×C25C2×D5
commutatorC2×C5C2×C4×C25
FrattiniC22×C5C2×C5×D5
FittingC23×C5×C25C2
socle, cosocleC22×C52C22×C5
prime radicalC23×C52C2×C5
hypercenterC23×C25D5
hypocenterC5C22⋊C4×C25
LCSG ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C25 ◁ C23×C25

166 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 200

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2000, 175);