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C4×C5×#10597244 #27130867

order12100
automorphism?
homologyAbelianization (H1) = C4×C52 · Schur multiplier (H2) = C5

Aliases

direct productC4×C5×#10597244

Splittings

FittingC4×C5×C112 ⋊ C5
derived, SylowC112 ⋊ C4×C52
HallC4×C112 ⋊ C52

Subgroups

subgroupG/H
center, hypercenterC4×C5#10597244
commutator, hypocenterC112C4×C52
FrattiniC2C2×C5×#10597244
FittingC4×C5×C112C5
socleC2×C5×C112C2×C5
prime radicalC2×C5×#10597244C2
cosocleC2×C112C2×C52
LCSG ▷ C112
UCSC1 ◁ C4×C5

108 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

580 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC5×Dic3×#10597244, C3×C4×C5×#10597244
maximal normal subgroup ofC3×C4×C5×#10597244
maximal quotient ofC5×Dic3×#10597244, C3×C4×C5×#10597244

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12100, 146);