Finite Group Databasebeta

← Prev (#27130751) Next (#27130753) →

C2×D5×C121⋊C5 #27130752

order12100
automorphism?
homologyAbelianization (H1) = C22×C5 · Schur multiplier (H2) = C2

Aliases

direct productC2×D5×C121⋊C5
unambiguous semidirect productC5⋊(C22×C121⋊C5)
unambiguous semidirect product(C2×C5)⋊(C2×C121⋊C5)
unambiguous semidirect product(C2×D5×C121)⋊C5

Splittings

FittingC2×C5×C121 ⋊ C2×C5
derivedC5×C121 ⋊ C22×C5
HallC5×C121⋊C5 ⋊ C22
SylowC121 ⋊ C2×C5×D5

Subgroups

subgroupG/H
center, hypercenterC2D5×C121⋊C5
commutator, cosocle, hypocenterC5×C121C22×C5
FrattiniC11C2×D5×C11⋊C5
FittingC2×C5×C121C2×C5
socleC2×C5×C11C2×C11⋊C5
LCSG ▷ C5×C121
UCSC1 ◁ C2

72 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

232 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×D5×C121⋊C5, C2×C3×D5×C121⋊C5, C2×D15×C121⋊C5
maximal normal subgroup ofC2×C3×D5×C121⋊C5
maximal quotient ofD3×D5×C121⋊C5, C2×C3×D5×C121⋊C5, C2×D15×C121⋊C5

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12100, 31);