Finite Group Databasebeta

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C5×#10610272 #72223027

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

Aliases

direct productC5×#10610272

Splittings

FittingC4×C52×M16 ⋊ C2
SylowC52 ⋊ #2956

Subgroups

subgroupG/H
centerC4×C5C22×D20
commutatorC4×C5C23×C4×C5
FrattiniC2×C4C23×C5×D5
FittingC4×C52×M16C2
socleC2×C52C2×C4×D4
prime radicalC5×#66082C2
cosocleC2×C4×C5C24×C5
hypercenterC4×C5×M16D5
hypocenterC5C5×#2956
LCSG ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C4×C5 ◁ C2×C5×M16 ◁ C4×C5×M16

1058 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

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

Relationships

maximal subgroup of#72223041, C5×#12975606, #72227631
maximal normal subgroup of#72223041, C5×#12975606, #72227631

GAP

Past the SmallGroups library coverage — no SmallGroups id.