Finite Group Databasebeta

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C2×C5×C5⋊((C11⋊D11)⋊C3) #49137698

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

Aliases

direct productC2×C5×C5⋊((C11⋊D11)⋊C3)
unambiguous semidirect product(C2×C5)⋊(C5×(C11⋊D11)⋊C3)
unambiguous semidirect product(C2×C5×C5⋊(C11⋊D11))⋊C3

Splittings

Fitting, socleC2×C52×C112 ⋊ C2×C3
derivedC5×C112 ⋊ C22×C3×C5
HallC2×C5×C5⋊(C11⋊D11) ⋊ C3
HallC52×C112⋊C3 ⋊ C22
HallC52×C112 ⋊ C22×C3
HallC112⋊C3 ⋊ C2×C5×D5
SylowC112 ⋊ C2×C3×C5×D5
SylowC52 ⋊ C2×(C11⋊D11)⋊C3

Subgroups

subgroupG/H
center, hypercenterC2×C5C5⋊((C11⋊D11)⋊C3)
commutator, cosocle, hypocenterC5×C112C22×C3×C5
FrattiniC1G
Fitting, socleC2×C52×C112C2×C3
LCSG ▷ C5×C112
UCSC1 ◁ C2×C5

192 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 660

Conjugacy classes & character table

1120 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36300, 834);