Finite Group Databasebeta

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C5×#87832 #14522668

order2000
isoclinismisoclinic class of #87831
automorphism?
homologyAbelianization (H1) = C2×C4×C5 · Schur multiplier (H2) = C2

Aliases

direct productC5×#87832

Splittings

SylowC53 ⋊ C4⋊C4

Subgroups

subgroupG/H
center, hypercenterC2×C5D5⋊AGL(1,𝔽5)
commutatorC2×C52C2×C4×C5
FrattiniC2C5×D5⋊AGL(1,𝔽5)
Fitting, socleC2×C53C2×C4
prime radicalC2×C5×C5⋊D5C22
cosocleC2×C5⋊D5C22×C5
hypocenterC52C5×C4⋊C4
LCSG ▷ C2×C52 ▷ C52
UCSC1 ◁ C2×C5

156 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 80

Conjugacy classes & character table

110 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD5×#87832, C5×#11717375, #72259203
maximal normal subgroup ofD5×#87832, C5×#11717375, #72259203

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2000, 631);