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C2×C5×C3⋊(D31⋊C5) #22604871

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

Aliases

direct productC2×C5×C3⋊(D31⋊C5)
unambiguous semidirect product(C2×C3)⋊(C5×D31⋊C5)
unambiguous semidirect product(C2×ΓL(1,𝔽32))⋊(C5×D3)
unambiguous semidirect product(C2×D93)⋊C52
unambiguous semidirect product(C2×C5×D93)⋊C5

Splittings

Fitting, socleC2×C3×C5×C31 ⋊ C2×C5
derived, HallC3×C31 ⋊ C22×C52
HallC3×C5×ΓL(1,𝔽32) ⋊ C22
HallC5×ΓL(1,𝔽32) ⋊ C2×D3
HallC2×D93 ⋊ C52
SylowC31 ⋊ C2×C52×D3
SylowC3 ⋊ C2×C5×D31⋊C5

Subgroups

subgroupG/H
center, hypercenterC2×C5C3⋊(D31⋊C5)
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

240 conjugacy classes — view the full character table.

Relationships

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9300, 145);