Finite Group Databasebeta

← Prev (#20258986) Next (#20258988) →

C2×C3×C3⋊(C13⋊D13) #20258987

order6084
automorphism?
homologyAbelianization (H1) = C22×C3 · Schur multiplier (H2) = C2×C13

Aliases

direct productC2×C3×C3⋊(C13⋊D13)
unambiguous semidirect product(C2×C3)⋊(C3×C13⋊D13)

Splittings

Fitting, socleC2×C32×C132 ⋊ C2
derivedC3×C132 ⋊ C22×C3
HallC32×C132 ⋊ C22
SylowC132 ⋊ C2×C3×D3
SylowC32 ⋊ C2×C13⋊D13

Subgroups

subgroupG/H
center, hypercenterC2×C3C3⋊(C13⋊D13)
commutator, hypocenterC3×C132C22×C3
FrattiniC1G
Fitting, socleC2×C32×C132C2
LCSG ▷ C3×C132
UCSC1 ◁ C2×C3

352 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1530 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC3×D5×C3⋊(C13⋊D13), C2×C3×C5×C3⋊(C13⋊D13), C2×C3×C3⋊(C5⋊(C13⋊D13))
maximal normal subgroup ofC2×C3×C5×C3⋊(C13⋊D13)
maximal quotient ofC3×D5×C3⋊(C13⋊D13), C2×C3×C5×C3⋊(C13⋊D13), C2×C3×C3⋊(C5⋊(C13⋊D13))

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(6084, 294);