Finite Group Databasebeta

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C5×C22⋊((C112⋊C3)⋊C5) #49137539

order36300
automorphism?
homologyAbelianization (H1) = C3×C52 · Schur multiplier (H2) = C2×C5

Aliases

direct productC5×C22⋊((C112⋊C3)⋊C5)
unambiguous semidirect productC22⋊(C5×(C112⋊C3)⋊C5)
unambiguous semidirect product(C22×C5)⋊((C112⋊C3)⋊C5)
unambiguous semidirect product(C22⋊(C112⋊C3))⋊C52
unambiguous semidirect product(C5×#10597243)⋊A4
unambiguous semidirect product(C5×C22⋊(C112⋊C3))⋊C5

Splittings

Fitting, socleC22×C5×C112 ⋊ C3×C5
derived, HallC22×C112 ⋊ C3×C52
HallC22×C5×#10597243 ⋊ C3
HallC5×#10597243 ⋊ A4
HallC22⋊(C112⋊C3) ⋊ C52
SylowC112 ⋊ C52×A4
SylowC22 ⋊ C5×(C112⋊C3)⋊C5

Subgroups

subgroupG/H
center, hypercenterC5C22⋊((C112⋊C3)⋊C5)
commutator, cosocle, hypocenterC22×C112C3×C52
FrattiniC1G
Fitting, socleC22×C5×C112C3×C5
LCSG ▷ C22×C112
UCSC1 ◁ C5

240 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 330

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36300, 675);