Finite Group Databasebeta

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C3×C7×C11×C5⋊D5 #26040545

order11550
isoclinismisoclinic class of C5⋊D5
automorphism?
homologyAbelianization (H1) = C2×C3×C7×C11 · Schur multiplier (H2) = C5

Aliases

direct productC3×C7×C11×C5⋊D5
unambiguous semidirect productC5⋊(C3×C7×D5×C11)

Splittings

Fitting, socle, HallC3×C52×C7×C11 ⋊ C2
derived, SylowC52 ⋊ C2×C3×C7×C11
HallC52×C7×C11 ⋊ C2×C3
HallC3×C52×C11 ⋊ C2×C7
HallC3×C52×C7 ⋊ C2×C11
HallC52×C11 ⋊ C2×C3×C7
HallC52×C7 ⋊ C2×C3×C11
HallC3×C52 ⋊ C2×C7×C11

Subgroups

subgroupG/H
center, hypercenterC3×C7×C11C5⋊D5
commutator, cosocle, hypocenterC52C2×C3×C7×C11
FrattiniC1G
Fitting, socleC3×C52×C7×C11C2
LCSG ▷ C52
UCSC1 ◁ C3×C7×C11

128 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3234 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC3×C7×D52×C11, C3×C7×(C5⋊D5)⋊D11, C3×C11×(C5⋊D5)⋊D7, …
maximal normal subgroup ofC3×C7×D52×C11, C3×C7×(C5⋊D5)⋊D11, C3×C11×(C5⋊D5)⋊D7, …
maximal quotient ofC3×C7×C11×#1039, C2×C3×C7×C11×C5⋊D5, C7×C9×C11×C5⋊D5, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11550, 109);