Finite Group Databasebeta

C25×#681 #14522174

order2000
isoclinismisoclinic class of Dic10
automorphism?
homologyAbelianization (H1) = C2×C4×C25 · Schur multiplier (H2) = C1

Aliases

direct productC25×#681

Splittings

SylowC5×C25 ⋊ M16

Subgroups

subgroupG/H
centerC4×C25C2×D5
commutatorC2×C5C2×C4×C25
FrattiniC4×C5C2×C5×D5
FittingC2×C4×C5×C25C2
socleC2×C52C2×C4×C5
prime radicalC22×C52C4×C5
cosocleC4×C52C22×C5
hypercenterC2×C4×C25D5
hypocenterC5M16×C25
LCSG ▷ C2×C5 ▷ C5
UCSC1 ◁ C4×C25 ◁ C2×C4×C25

92 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, 137);