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C2×C3×D5×C11⋊C5 #15693169

order3300
automorphism?
homologyAbelianization (H1) = C22×C3×C5 · Schur multiplier (H2) = C2

Aliases

direct productC2×C3×D5×C11⋊C5
unambiguous semidirect productC5⋊(C22×C3×C11⋊C5)
unambiguous semidirect product(C2×C5)⋊(C2×C3×C11⋊C5)
unambiguous semidirect product(C2×D5×C11)⋊(C3×C5)
unambiguous semidirect product(C2×C3×D5×C11)⋊C5

Splittings

Fitting, socleC2×C3×C5×C11 ⋊ C2×C5
derivedC5×C11 ⋊ C22×C3×C5
HallC3×C5×C11⋊C5 ⋊ C22
HallC5×C11⋊C5 ⋊ C22×C3
HallC3×C11 ⋊ C2×C5×D5
SylowC11 ⋊ C2×C3×C5×D5

Subgroups

subgroupG/H
center, hypercenterC2×C3D5×C11⋊C5
commutator, cosocle, hypocenterC5×C11C22×C3×C5
FrattiniC1G
Fitting, socleC2×C3×C5×C11C2×C5
LCSG ▷ C5×C11
UCSC1 ◁ C2×C3

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 330

Conjugacy classes & character table

168 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD5×AGL(1,𝔽7)×C11⋊C5, C2×C11⋊C5×C5⋊AGL(1,𝔽7), C2×D5×ΓL(1,𝔽8)×C11⋊C5, …
maximal normal subgroup ofC2×C3×C7×D5×C11⋊C5, C2×C3×D5×C11×C11⋊C5
maximal quotient ofD5×AGL(1,𝔽7)×C11⋊C5, C2×C11⋊C5×C5⋊AGL(1,𝔽7), C2×D5×ΓL(1,𝔽8)×C11⋊C5, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3300, 89);