Finite Group Databasebeta

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C2×C11×C3⋊(C5⋊D5) #15693231

order3300
isoclinismisoclinic class of C3⋊(C5⋊D5)
automorphism?
homologyAbelianization (H1) = C22×C11 · Schur multiplier (H2) = C2×C5

Aliases

direct productC2×C11×C3⋊(C5⋊D5)
unambiguous semidirect product(C2×C3)⋊(C11×C5⋊D5)
unambiguous semidirect product(C2×C5)⋊(C11×D15)

Splittings

Fitting, socleC2×C3×C52×C11 ⋊ C2
derived, HallC3×C52 ⋊ C22×C11
HallC3×C52×C11 ⋊ C22
HallC52×C11 ⋊ C2×D3
HallC3×C11 ⋊ C2×C5⋊D5
SylowC52 ⋊ C2×D3×C11
SylowC3 ⋊ C2×C11×C5⋊D5

Subgroups

subgroupG/H
center, hypercenterC2×C11C3⋊(C5⋊D5)
commutator, cosocle, hypocenterC3×C52C22×C11
FrattiniC1G
Fitting, socleC2×C3×C52×C11C2
LCSG ▷ C3×C52
UCSC1 ◁ C2×C11

160 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1650

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC11×D7×C3⋊(C5⋊D5), C2×C7×C11×C3⋊(C5⋊D5), C2×C11×C3⋊(C5⋊D35), …
maximal normal subgroup ofC2×C7×C11×C3⋊(C5⋊D5), C2×C121×C3⋊(C5⋊D5), C2×C112×C3⋊(C5⋊D5)
maximal quotient ofC11×D7×C3⋊(C5⋊D5), C2×C7×C11×C3⋊(C5⋊D5), C2×C11×C3⋊(C5⋊D35), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3300, 151);