Finite Group Databasebeta

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C2×C3×Dic25⋊C5 #72219015

order3000
isoclinismisoclinic class of D25⋊C5
automorphism?
homologyAbelianization (H1) = C2×C3×C4×C5 · Schur multiplier (H2) = C2

Aliases

direct productC2×C3×Dic25⋊C5

Splittings

derivedC25 ⋊ C2×C3×C4×C5
HallC3×5−1+2 ⋊ C2×C4
Sylow5−1+2 ⋊ C2×C3×C4

Subgroups

subgroupG/H
center, hypercenterC22×C3D25⋊C5
commutator, hypocenterC25C2×C3×C4×C5
FrattiniC2×C5C2×C3×C5×D5
FittingC22×C3×5−1+2C2
socleC22×C3×C5C5×D5
prime radicalC22×C3×C52D5
cosocleC2×C25C22×C3×C5
LCSG ▷ C25
UCSC1 ◁ C22×C3

116 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC2×C3×C4×D25⋊C5
maximal normal subgroup ofC2×C3×C4×D25⋊C5

GAP

Past the SmallGroups library coverage — no SmallGroups id.