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C2×C3×C13×D33 #19104248

order5148
isoclinismisoclinic class of D33
automorphism?
homologyAbelianization (H1) = C22×C3×C13 · Schur multiplier (H2) = C2

Aliases

direct productC2×C3×C13×D33
unambiguous semidirect product(C2×C3)⋊(C3×C13×D11)
unambiguous semidirect product(C2×C11)⋊(C3×D3×C13)

Splittings

Fitting, socleC2×C32×C11×C13 ⋊ C2
derivedC3×C11 ⋊ C22×C3×C13
HallC32×C11×C13 ⋊ C22
HallC11×C13 ⋊ C2×C3×D3
HallC32×C13 ⋊ C2×D11
HallC32×C11 ⋊ C22×C13
SylowC11 ⋊ C2×C3×D3×C13
SylowC32 ⋊ C2×C13×D11

Subgroups

subgroupG/H
center, hypercenterC2×C3×C13D33
commutator, hypocenterC3×C11C22×C3×C13
FrattiniC1G
Fitting, socleC2×C32×C11×C13C2
LCSG ▷ C3×C11
UCSC1 ◁ C2×C3×C13

88 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1404 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C3×C13×C3⋊AGL(1,𝔽11), C3×D5×C13×D33, C2×C3×C5×C13×D33, …
maximal normal subgroup ofC2×C3×C13×C3⋊AGL(1,𝔽11), C2×C3×C5×C13×D33, C2×C3×C7×C13×D33
maximal quotient ofC3×D5×C13×D33, C2×C3×C5×C13×D33, C2×C3×C13×D165, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5148, 124);