Finite Group Databasebeta

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C3×#11751705 #72230451

order2880
automorphism?
homologyAbelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C23

Aliases

direct productC3×#11751705

Splittings

HallC32×C5 ⋊ #417
SylowC32 ⋊ #65793
SylowC5 ⋊ C3×#4966

Subgroups

subgroupG/H
centerC2×C3C2×(C2×D3)⋊AGL(1,𝔽5)
commutatorC3×C4×C5C22×C3×C4
FrattiniC4C2×C3×D3×AGL(1,𝔽5)
FittingC2×C32×C4×C5C2×C4
socleC2×C32×C5C2×C22⋊C4
prime radicalC3×D5×#235C2
cosocleC3×C4×D5C23×C3
hypercenterC2×C3×C4D3×AGL(1,𝔽5)
hypocenterC3×C5C3×#417
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C3 ◁ C2×C3×C4

740 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 120

Conjugacy classes & character table

180 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#72230455, C3×AGL(1,𝔽5)×#932, #72230464
maximal normal subgroup of#72230455, C3×AGL(1,𝔽5)×#932, #72230464

GAP

Past the SmallGroups library coverage — no SmallGroups id.