Finite Group Databasebeta

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C4×C5×#10597243 #27130865

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

Aliases

direct productC4×C5×#10597243

Splittings

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

Subgroups

subgroupG/H
center, hypercenterC4×C5#10597243
commutator, hypocenterC112C4×C52
FrattiniC2C2×C5×#10597243
FittingC4×C5×C112C5
socleC2×C5×C112C2×C5
prime radicalC2×C5×#10597243C2
cosocleC2×C112C2×C52
LCSG ▷ C112
UCSC1 ◁ C4×C5

336 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

580 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC4×C5×(C112⋊C3)⋊C5, C5×Dic3×#10597243, C3×C4×C5×#10597243
maximal normal subgroup ofC4×C5×(C112⋊C3)⋊C5, C3×C4×C5×#10597243
maximal quotient ofC5×Dic3×#10597243, C3×C4×C5×#10597243

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12100, 144);