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C2×C7×C13×D33 #26046589

order12012
isoclinismisoclinic class of D33
automorphism?
homologyAbelianization (H1) = C22×C7×C13 · Schur multiplier (H2) = C2

Aliases

direct productC2×C7×C13×D33
unambiguous semidirect product(C2×C3)⋊(C7×C13×D11)
unambiguous semidirect product(C2×C11)⋊(D3×C7×C13)

Splittings

Fitting, socleC2×C3×C7×C11×C13 ⋊ C2
derived, HallC3×C11 ⋊ C22×C7×C13
HallC3×C7×C11×C13 ⋊ C22
HallC7×C11×C13 ⋊ C2×D3
HallC3×C11×C13 ⋊ C22×C7
HallC3×C7×C13 ⋊ C2×D11
HallC3×C7×C11 ⋊ C22×C13
HallC11×C13 ⋊ C2×D3×C7
HallC7×C11 ⋊ C2×D3×C13
HallC3×C13 ⋊ C2×C7×D11
HallC3×C7 ⋊ C2×C13×D11
SylowC11 ⋊ C2×D3×C7×C13
SylowC3 ⋊ C2×C7×C13×D11

Subgroups

subgroupG/H
center, hypercenterC2×C7×C13D33
commutator, cosocle, hypocenterC3×C11C22×C7×C13
FrattiniC1G
Fitting, socleC2×C3×C7×C11×C13C2
LCSG ▷ C3×C11
UCSC1 ◁ C2×C7×C13

80 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3276 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C7×C13×D99, C2×C7×C13⋊C3×D33, C2×C13×ΓL(1,𝔽8)×D33, …
maximal normal subgroup ofC2×C7×C13⋊C3×D33, C2×C13×ΓL(1,𝔽8)×D33, C2×D33×#63270, …
maximal quotient ofC2×C7×C13×D99, D3×C7×C13×D33, C2×C3×C7×C13×D33, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12012, 179);