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C2×C3×C5×C11×D11 #20300131

order7260
isoclinismisoclinic class of D11
automorphism?
homologyAbelianization (H1) = C22×C3×C5×C11 · Schur multiplier (H2) = C2

Aliases

direct productC2×C3×C5×C11×D11

Splittings

Fitting, socleC2×C3×C5×C112 ⋊ C2
derivedC11 ⋊ C22×C3×C5×C11
HallC3×C5×C112 ⋊ C22
HallC5×C112 ⋊ C22×C3
HallC3×C112 ⋊ C22×C5
SylowC112 ⋊ C22×C3×C5

Subgroups

subgroupG/H
center, hypercenterC2×C3×C5×C11D11
commutator, hypocenterC11C22×C3×C5×C11
FrattiniC1G
Fitting, socleC2×C3×C5×C112C2
LCSG ▷ C11
UCSC1 ◁ C2×C3×C5×C11

120 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2310 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C5×C9×C11×D11, C2×C3×C5×#10624391, C3×C5×D3×C11×D11, …
maximal normal subgroup ofC2×C5×C9×C11×D11, C2×C32×C5×C11×D11, C2×C3×C11×D11⋊C25, …
maximal quotient ofC2×C5×C9×C11×D11, C3×C5×D3×C11×D11, C2×C32×C5×C11×D11, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7260, 231);