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D3×C5⋊D5×C121 #49136992

order36300
automorphism?
homologyAbelianization (H1) = C22×C121 · Schur multiplier (H2) = C2×C5

Aliases

direct productD3×C5⋊D5×C121
unambiguous semidirect product(C5×D3)⋊(D5×C121)

Splittings

Fitting, HallC3×C52×C121 ⋊ C22
derived, HallC3×C52 ⋊ C22×C121
HallC52×C121 ⋊ C2×D3
HallC3×C121 ⋊ C2×C5⋊D5
SylowC52 ⋊ C2×D3×C121
SylowC3 ⋊ C2×C5⋊D5×C121

Subgroups

subgroupG/H
center, hypercenterC121D3×C5⋊D5
commutator, hypocenterC3×C52C22×C121
FrattiniC11D3×C11×C5⋊D5
FittingC3×C52×C121C22
socle, cosocleC3×C52×C11C22×C11
prime radicalD3×C11×C5⋊D5C11
LCSG ▷ C3×C52
UCSC1 ◁ C121

240 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9075

Conjugacy classes & character table

5082 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36300, 128);