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C2×C11×C3⋊(D13⋊C3) #19104201

order5148
isoclinismisoclinic class of C3⋊(D13⋊C3)
automorphism?
homologyAbelianization (H1) = C22×C3×C11 · Schur multiplier (H2) = C2

Aliases

direct productC2×C11×C3⋊(D13⋊C3)
unambiguous semidirect product(C2×C3)⋊(C11×D13⋊C3)
unambiguous semidirect product(C2×C13⋊C3)⋊(D3×C11)
unambiguous semidirect product(C2×D39)⋊(C3×C11)
unambiguous semidirect product(C2×C11×D39)⋊C3

Splittings

Fitting, socleC2×C3×C11×C13 ⋊ C2×C3
derivedC3×C13 ⋊ C22×C3×C11
HallC3×C11×C13⋊C3 ⋊ C22
HallC11×C13 ⋊ C2×C3×D3
HallC3×C13⋊C3 ⋊ C22×C11
SylowC13 ⋊ C2×C3×D3×C11

Subgroups

subgroupG/H
center, hypercenterC2×C11C3⋊(D13⋊C3)
commutator, hypocenterC3×C13C22×C3×C11
FrattiniC1G
Fitting, socleC2×C3×C11×C13C2×C3
LCSG ▷ C3×C13
UCSC1 ◁ C2×C11

88 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

330 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×C11⋊C5×C3⋊(D13⋊C3), D5×C11×C3⋊(D13⋊C3), C2×C5×C11×C3⋊(D13⋊C3), …
maximal normal subgroup ofC2×C11⋊C5×C3⋊(D13⋊C3), C2×C5×C11×C3⋊(D13⋊C3), C2×C7×C11×C3⋊(D13⋊C3)
maximal quotient ofD5×C11×C3⋊(D13⋊C3), C2×C5×C11×C3⋊(D13⋊C3), C2×C11×C3⋊(C5⋊(D13⋊C3)), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5148, 77);