Finite Group Databasebeta

← Prev (#72223429) Next (#72223431) →

C5×#10610711 #72223430

order3200
automorphism?
homologyAbelianization (H1) = C23×C4×C5 · Schur multiplier (H2) = C25

Aliases

direct productC5×#10610711

Splittings

FittingC2×C52×#104 ⋊ C2
SylowC52 ⋊ #2956

Subgroups

subgroupG/H
centerC4×C5C2×D4×D5
commutatorC4×C5C23×C4×C5
FrattiniC2×C4C23×C5×D5
FittingC2×C52×#104C2
socleC2×C52C2×C4×D4
prime radicalC5×#66156C2
cosocleC2×C4×C5C24×C5
hypercenterC2×C5×#104D5
hypocenterC5C5×#2956
LCSG ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C4×C5 ◁ C22×C4×C5 ◁ C2×C5×#104

1086 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

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

Relationships

maximal subgroup of#72223437
maximal normal subgroup of#72223437

GAP

Past the SmallGroups library coverage — no SmallGroups id.