Finite Group Databasebeta

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C11×C3⋊(C3⋊(C5⋊D5)) #19097136

order4950
isoclinismisoclinic class of C3⋊(C3⋊(C5⋊D5))
automorphism?
homologyAbelianization (H1) = C2×C11 · Schur multiplier (H2) = C3×C5

Aliases

direct productC11×C3⋊(C3⋊(C5⋊D5))
unambiguous semidirect productC3⋊(C11×C3⋊(C5⋊D5))
unambiguous semidirect productC5⋊(C11×C3⋊D15)

Splittings

Fitting, socle, HallC32×C52×C11 ⋊ C2
derived, HallC32×C52 ⋊ C2×C11
HallC52×C11 ⋊ C3⋊D3
HallC32×C11 ⋊ C5⋊D5
SylowC52 ⋊ C11×C3⋊D3
SylowC32 ⋊ C11×C5⋊D5

Subgroups

subgroupG/H
center, hypercenterC11C3⋊(C3⋊(C5⋊D5))
commutator, hypocenterC32×C52C2×C11
FrattiniC1G
Fitting, socleC32×C52×C11C2
LCSG ▷ C32×C52
UCSC1 ◁ C11

192 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1254 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC7×C11×C3⋊(C3⋊(C5⋊D5)), C11×C3⋊(C3⋊(C5⋊D35))
maximal normal subgroup ofC7×C11×C3⋊(C3⋊(C5⋊D5))
maximal quotient ofC7×C11×C3⋊(C3⋊(C5⋊D5)), C11×C3⋊(C3⋊(C5⋊D35))

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4950, 97);