Finite Group Databasebeta

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C2×C11×C13⋊(C52⋊C3) #36339768

order21450
automorphism?
homologyAbelianization (H1) = C2×C3×C11 · Schur multiplier (H2) = C5

Aliases

direct productC2×C11×C13⋊(C52⋊C3)
unambiguous semidirect product(C2×C13)⋊(C11×C52⋊C3)
unambiguous semidirect product(C2×C52)⋊(C11×C13⋊C3)
unambiguous semidirect product(C2×C11×C13)⋊(C52⋊C3)
unambiguous semidirect product(C2×C52×C11)⋊(C13⋊C3)

Splittings

Fitting, socle, HallC2×C52×C11×C13 ⋊ C3
derived, HallC52×C13 ⋊ C2×C3×C11
HallC52×C11×C13 ⋊ C2×C3
HallC2×C52×C13 ⋊ C3×C11
HallC2×C52×C11 ⋊ C13⋊C3
HallC2×C11×C13 ⋊ C52⋊C3
HallC52×C11 ⋊ C2×C13⋊C3
HallC11×C13 ⋊ C2×C52⋊C3
HallC2×C52 ⋊ C11×C13⋊C3
HallC2×C13 ⋊ C11×C52⋊C3
SylowC52 ⋊ C2×C11×C13⋊C3
SylowC13 ⋊ C2×C11×C52⋊C3

Subgroups

subgroupG/H
center, hypercenterC2×C11C13⋊(C52⋊C3)
commutator, cosocle, hypocenterC52×C13C2×C3×C11
FrattiniC1G
Fitting, socleC2×C52×C11×C13C3
LCSG ▷ C52×C13
UCSC1 ◁ C2×C11

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4290

Conjugacy classes & character table

2442 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21450, 92);