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C2×C4×D3×C11 #10587267

order528
isoclinismisoclinic class of D3
automorphism?
homologyAbelianization (H1) = C22×C4×C11 · Schur multiplier (H2) = C23

Aliases

direct productC2×C4×D3×C11

Splittings

FittingC2×C3×C4×C11 ⋊ C2
derived, SylowC3 ⋊ C22×C4×C11
HallC3×C11 ⋊ C22×C4

Subgroups

subgroupG/H
center, hypercenterC2×C4×C11D3
commutator, hypocenterC3C22×C4×C11
FrattiniC2C22×D3×C11
FittingC2×C3×C4×C11C2
socleC22×C3×C11C22
prime radicalC22×D3×C11C2
cosocleC2×C3C23×C11
LCSG ▷ C3
UCSC1 ◁ C2×C4×C11

108 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 264

Conjugacy classes & character table

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

Relationships

maximal subgroup of(C2×D3)⋊(C11⋊C8), C11×(C2×D3)⋊C8, #11760739, …
maximal normal subgroup of(C2×D3)⋊(C11⋊C8), C11×(C2×D3)⋊C8, #11760739, …
maximal quotient ofC4×C11×Dic6, C42×D3×C11, C11×#872, …
automorphism group ofC22×C5×C23
outer automorphism group ofC22×C5×C23

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(528, 137);