Finite Group Databasebeta

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C2×C11×D11×C52⋊C3 #49137683

order36300
automorphism?
homologyAbelianization (H1) = C22×C3×C11 · Schur multiplier (H2) = C2×C5

Aliases

direct productC2×C11×D11×C52⋊C3
unambiguous semidirect productC11⋊(C22×C11×C52⋊C3)
unambiguous semidirect product(C2×C11)⋊(C2×C11×C52⋊C3)
unambiguous semidirect product(C2×C52×D11)⋊(C3×C11)
unambiguous semidirect product(C2×C52×C11×D11)⋊C3

Splittings

Fitting, socleC2×C52×C112 ⋊ C2×C3
derivedC52×C11 ⋊ C22×C3×C11
HallC2×C52×C11×D11 ⋊ C3
HallC112×C52⋊C3 ⋊ C22
HallC52×C112 ⋊ C22×C3
SylowC112 ⋊ C22×C52⋊C3
SylowC52 ⋊ C2×C3×C11×D11

Subgroups

subgroupG/H
center, hypercenterC2×C11D11×C52⋊C3
commutator, cosocle, hypocenterC52×C11C22×C3×C11
FrattiniC1G
Fitting, socleC2×C52×C112C2×C3
LCSG ▷ C52×C11
UCSC1 ◁ C2×C11

180 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 660

Conjugacy classes & character table

1694 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36300, 819);