Finite Group Databasebeta

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C2×C5⋊(((C11⋊D11)⋊C3)⋊C5) #49137363

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

Aliases

direct productC2×C5⋊(((C11⋊D11)⋊C3)⋊C5)
unambiguous semidirect product(C2×C5)⋊(((C11⋊D11)⋊C3)⋊C5)
unambiguous semidirect product(C2×C5⋊((C11⋊D11)⋊C3))⋊C5
unambiguous semidirect product(C2×C5⋊#11925892)⋊C3

Splittings

Fitting, socleC2×C5×C112 ⋊ C2×C3×C5
derivedC5×C112 ⋊ C22×C3×C5
HallC2×C5⋊#11925892 ⋊ C3
HallC5×(C112⋊C3)⋊C5 ⋊ C22
HallC5×#10597243 ⋊ C22×C3
HallC112⋊C3 ⋊ C2×C5×D5
SylowC112 ⋊ C2×C3×C5×D5

Subgroups

subgroupG/H
center, hypercenterC2C5⋊(((C11⋊D11)⋊C3)⋊C5)
commutator, cosocle, hypocenterC5×C112C22×C3×C5
FrattiniC1G
Fitting, socleC2×C5×C112C2×C3×C5
LCSG ▷ C5×C112
UCSC1 ◁ C2

192 conjugacy classes of subgroups; only the 32 normal subgroups are shown.

normal subgroups only

This group has 192 conjugacy classes of subgroups — too many to draw. Only its 32 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

transitive degreeμt(G) = 330

Conjugacy classes & character table

160 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36300, 499);