Finite Group Databasebeta

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C25×#700 #14522312

order2000
isoclinismisoclinic class of #700
automorphism?
homologyAbelianization (H1) = C2×C4×C25 · Schur multiplier (H2) = C1

Aliases

direct productC25×#700

Splittings

SylowC5×C25 ⋊ M16

Subgroups

subgroupG/H
centerC2×C25C2×AGL(1,𝔽5)
commutatorC2×C5C2×C4×C25
FrattiniC2×C5C2×C5×AGL(1,𝔽5)
FittingC4×C5×C25C4
socleC2×C52C2×C4×C5
prime radicalC2×C5×D5C4×C5
cosocleC5×Dic5C22×C5
hypercenterC4×C25AGL(1,𝔽5)
hypocenterC5M16×C25
LCSG ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C25 ◁ C4×C25

66 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 400

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2000, 275);