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C2×C3⋊(C5⋊(D31⋊C5)) #22604873

order9300
automorphism?
homologyAbelianization (H1) = C22×C5 · Schur multiplier (H2) = C2

Aliases

direct productC2×C3⋊(C5⋊(D31⋊C5))
unambiguous semidirect product(C2×C3)⋊(C5⋊(D31⋊C5))
unambiguous semidirect product(C2×C5)⋊(C3⋊(D31⋊C5))
unambiguous semidirect product(C2×ΓL(1,𝔽32))⋊D15
unambiguous semidirect product(C2×D465)⋊C5

Splittings

Fitting, socleC2×C3×C5×C31 ⋊ C2×C5
derivedC3×C5×C31 ⋊ C22×C5
HallC3×C5×ΓL(1,𝔽32) ⋊ C22
HallC5×ΓL(1,𝔽32) ⋊ C2×D3
HallC3×C31 ⋊ C2×C5×D5
SylowC31 ⋊ C2×C5×D15
SylowC3 ⋊ C2×C5⋊(D31⋊C5)

Subgroups

subgroupG/H
center, hypercenterC2C3⋊(C5⋊(D31⋊C5))
commutator, hypocenterC3×C5×C31C22×C5
FrattiniC1G
Fitting, socleC2×C3×C5×C31C2×C5
LCSG ▷ C3×C5×C31
UCSC1 ◁ C2

96 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

180 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×C5⋊(C9⋊(D31⋊C5)), C2×C3⋊(C5⋊AGL(1,𝔽31)), D3×C3⋊(C5⋊(D31⋊C5)), …
maximal normal subgroup ofC2×C3⋊(C5⋊AGL(1,𝔽31)), C2×C3×C3⋊(C5⋊(D31⋊C5))
maximal quotient ofC2×C5⋊(C9⋊(D31⋊C5)), D3×C3⋊(C5⋊(D31⋊C5)), C2×C3×C3⋊(C5⋊(D31⋊C5)), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9300, 147);