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C3×#92537⋊C2 #72219002

order3000
automorphism?
homologyAbelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C2

Aliases

direct productC3×#92537⋊C2

Splittings

Fitting, HallC3×H(3,𝔽5) ⋊ C2×C4
derived, SylowH(3,𝔽5) ⋊ C2×C3×C4

Subgroups

subgroupG/H
center, hypercenterC3#92537⋊C2
commutator, hypocenterH(3,𝔽5)C2×C3×C4
FrattiniC5C3×D5⋊AGL(1,𝔽5)
FittingC3×H(3,𝔽5)C2×C4
socleC3×C5D5⋊AGL(1,𝔽5)
prime radicalC3×((C5⋊D5)⋊C5)⋊C2C2
cosocle#6953C22×C3
LCSG ▷ H(3,𝔽5)
UCSC1 ◁ C3

136 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

66 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×#14522510, C2×C3×#92537⋊C2
maximal normal subgroup ofC3×#14522510, C2×C3×#92537⋊C2
maximal quotient ofC2×C3×#92537⋊C2

GAP

Past the SmallGroups library coverage — no SmallGroups id.