Finite Group Databasebeta

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C5×#10590393 #72260136

order2880
automorphism?
homologyAbelianization (H1) = C22×C4×C5 · Schur multiplier (H2) = C23

Aliases

direct productC5×#10590393

Splittings

FittingC32×C42×C5 ⋊ C22
HallC32×C5 ⋊ C2×#104
SylowC32 ⋊ C2×C5×#104

Subgroups

subgroupG/H
centerC4×C5#3802
commutatorC32×C4C22×C4×C5
FrattiniC2×C4C2×C5×D32
FittingC32×C42×C5C22
socleC2×C32×C5C2×C22⋊C4
prime radicalC5×#64306C2
cosocleC2×C32×C4C23×C5
hypercenterC42×C5D32
hypocenterC32C2×C5×#104
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4×C5 ◁ C2×C4×C5 ◁ C42×C5

788 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 120

Conjugacy classes & character table

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

Relationships

maximal subgroup ofD5×#10590393
maximal normal subgroup ofD5×#10590393

GAP

Past the SmallGroups library coverage — no SmallGroups id.