Finite Group Databasebeta

← Prev (#72231195) Next (#72231197) →

C3×#72231051 #72231196

order14400
automorphism?
homologyAbelianization (H1) = C2×C3×C42 · Schur multiplier (H2) = C2×C4

Aliases

direct productC3×#72231051

Splittings

HallC32×C52 ⋊ C4×M16
SylowC52 ⋊ C3×C4×#208
SylowC32 ⋊ #13107464

Subgroups

subgroupG/H
centerC2×C3C2×ΓL(1,𝔽16)⋊AGL(1,𝔽5)
commutatorC2×C3×C52C2×C3×C42
FrattiniC2C2×C3×ΓL(1,𝔽16)⋊AGL(1,𝔽5)
FittingC22×C32×C52C42
socleC2×C32×C52C2×C42
prime radicalC22×C32×C5⋊D5C2×C4
cosocleC3×#6036C23×C3
hypercenterC22×C3ΓL(1,𝔽16)⋊AGL(1,𝔽5)
hypocenterC3×C52C3×C4×M16
LCSG ▷ C2×C3×C52 ▷ C3×C52
UCSC1 ◁ C2×C3 ◁ C22×C3

1514 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 120

Conjugacy classes & character table

360 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of#72231278
maximal normal subgroup of#72231278

GAP

Past the SmallGroups library coverage — no SmallGroups id.