Finite Group Databasebeta

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C5×D5×#104 #13102081

order1600
automorphism?
homologyAbelianization (H1) = C22×C4×C5 · Schur multiplier (H2) = C23

Aliases

direct productC5×D5×#104

Splittings

FittingC52×#104 ⋊ C2
SylowC52 ⋊ C2×#104

Subgroups

subgroupG/H
centerC4×C5D4×D5
commutatorC4×C5C22×C4×C5
FrattiniC2×C4C22×C5×D5
FittingC52×#104C2
socleC2×C52C2×C22⋊C4
prime radicalC5×D5×#41C2
cosocleC2×C4×C5C23×C5
hypercenterC5×#104D5
hypocenterC5C2×C5×#104
LCSG ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C4×C5 ◁ C2×C4×C5 ◁ C5×#104

384 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 80

Conjugacy classes & character table

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

Relationships

maximal subgroup ofD52×#104, C5×AGL(1,𝔽5)×#104, C5×D5×#453, …
maximal normal subgroup ofD52×#104, C5×AGL(1,𝔽5)×#104, C5×D5×#453, …
maximal quotient of#104×D25⋊C5

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1600, 4433);