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C22×C3×C5×C11⋊C5 #15693179

order3300
isoclinismisoclinic class of C11⋊C5
automorphism?
homologyAbelianization (H1) = C22×C3×C52 · Schur multiplier (H2) = C2×C5

Aliases

direct productC22×C3×C5×C11⋊C5
unambiguous semidirect product(C22×C3×C11)⋊C52
unambiguous semidirect product(C22×C3×C5×C11)⋊C5

Splittings

Fitting, socleC22×C3×C5×C11 ⋊ C5
derived, SylowC11 ⋊ C22×C3×C52
HallC22×C3×C11 ⋊ C52
HallC22×C11 ⋊ C3×C52
HallC3×C11 ⋊ C22×C52

Subgroups

subgroupG/H
center, hypercenterC22×C3×C5C11⋊C5
commutator, cosocle, hypocenterC11C22×C3×C52
FrattiniC1G
Fitting, socleC22×C3×C5×C11C5
LCSG ▷ C11
UCSC1 ◁ C22×C3×C5

160 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 660

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC2×C5×AGL(1,𝔽7)×C11⋊C5, C22×C5×ΓL(1,𝔽8)×C11⋊C5, C2×C3×C5×D7×C11⋊C5, …
maximal normal subgroup ofC22×C3×C5×C7×C11⋊C5, C22×C3×C5×C11×C11⋊C5
maximal quotient ofC2×C5×AGL(1,𝔽7)×C11⋊C5, C22×C5×ΓL(1,𝔽8)×C11⋊C5, C2×C3×C5×D7×C11⋊C5, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3300, 99);