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C2×C5×D3×ΓL(1,𝔽32) #22604872

order9300
automorphism?
homologyAbelianization (H1) = C22×C52 · Schur multiplier (H2) = C2×C5

Aliases

direct productC2×C5×D3×ΓL(1,𝔽32)
unambiguous semidirect productC3⋊(C22×C5×ΓL(1,𝔽32))
unambiguous semidirect product(C2×C3)⋊(C2×C5×ΓL(1,𝔽32))
unambiguous semidirect product(C2×D3×C31)⋊C52
unambiguous semidirect product(C2×C5×D3×C31)⋊C5

Splittings

Fitting, socleC2×C3×C5×C31 ⋊ C2×C5
derived, HallC3×C31 ⋊ C22×C52
HallC3×C5×ΓL(1,𝔽32) ⋊ C22
HallC2×D3×C31 ⋊ C52
SylowC31 ⋊ C2×C52×D3
SylowC3 ⋊ C22×C5×ΓL(1,𝔽32)

Subgroups

subgroupG/H
center, hypercenterC2×C5D3×ΓL(1,𝔽32)
commutator, hypocenterC3×C31C22×C52
FrattiniC1G
Fitting, socleC2×C3×C5×C31C2×C5
LCSG ▷ C3×C31
UCSC1 ◁ C2×C5

160 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

330 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×C5×D9×ΓL(1,𝔽32), C2×C5×D3×(C31⋊C3)⋊C5, C5×D32×ΓL(1,𝔽32), …
maximal normal subgroup ofC2×C5×D3×(C31⋊C3)⋊C5, C2×C3×C5×D3×ΓL(1,𝔽32)
maximal quotient ofC2×C5×D9×ΓL(1,𝔽32), C5×D32×ΓL(1,𝔽32), C2×C3×C5×D3×ΓL(1,𝔽32), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9300, 146);