Finite Group Databasebeta

← Prev (#27130997) Next (#27130999) →

C2×C5⋊(C5⋊(C11⋊D11)) #27130998

order12100
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2×C5×C11

Aliases

direct productC2×C5⋊(C5⋊(C11⋊D11))
unambiguous semidirect product(C2×C5)⋊(C5⋊(C11⋊D11))
unambiguous semidirect product(C2×C11)⋊(C5⋊D55)

Splittings

Fitting, socleC2×C52×C112 ⋊ C2
derived, HallC52×C112 ⋊ C22
SylowC112 ⋊ C2×C5⋊D5
SylowC52 ⋊ C2×C11⋊D11

Subgroups

subgroupG/H
center, hypercenterC2C5⋊(C5⋊(C11⋊D11))
commutator, cosocle, hypocenterC52×C112C22
FrattiniC1G
Fitting, socleC2×C52×C112C2
LCSG ▷ C52×C112
UCSC1 ◁ C2

560 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3028 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×#31827692, C2×C11⋊(C11⋊((C5⋊D5)⋊C3)), C2×C5⋊(C5⋊((C11⋊D11)⋊C3)), …
maximal normal subgroup ofC2×#31827692, C2×C11⋊(C11⋊((C5⋊D5)⋊C3)), C2×C5⋊(C5⋊((C11⋊D11)⋊C3)), …
maximal quotient ofD3×C5⋊(C5⋊(C11⋊D11)), C2×C3×C5⋊(C5⋊(C11⋊D11)), C2×C3⋊(C5⋊(C5⋊(C11⋊D11)))

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12100, 277);