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C2×C11×D11⋊C25 #27130802

order12100
automorphism?
homologyAbelianization (H1) = C22×C11×C25 · Schur multiplier (H2) = C2

Aliases

direct productC2×C11×D11⋊C25
unambiguous semidirect productD11⋊(C2×C11×C25)
unambiguous semidirect product(C2×D11)⋊(C11×C25)
unambiguous semidirect product(C11⋊C25)⋊(C22×C11)
unambiguous semidirect product(C2×C11⋊C25)⋊(C2×C11)

Splittings

derivedC11 ⋊ C22×C11×C25
HallC11×C11⋊C25 ⋊ C22
HallC2×C11×D11 ⋊ C25
SylowC112 ⋊ C22×C25

Subgroups

subgroupG/H
center, hypercenterC2×C5×C11AGL(1,𝔽11)
commutator, hypocenterC11C22×C11×C25
FrattiniC5C2×C11×AGL(1,𝔽11)
Fitting, socleC2×C5×C112C2×C5
prime radicalC2×C5×C11×D11C5
cosocleC5×C11C22×C5×C11
LCSG ▷ C11
UCSC1 ◁ C2×C5×C11

64 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1210 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofD3×C11×D11⋊C25, C2×C3×C11×D11⋊C25, C2×C11×C3⋊(D11⋊C25)
maximal normal subgroup ofC2×C3×C11×D11⋊C25
maximal quotient ofD3×C11×D11⋊C25, C2×C3×C11×D11⋊C25, C2×C11×C3⋊(D11⋊C25)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12100, 81);