Finite Group Databasebeta

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C3×AGL(1,𝔽5)×#624 #72254754

order4320
automorphism?
homologyAbelianization (H1) = C2×C3×C42 · Schur multiplier (H2) = C22×C4

Aliases

direct productC3×AGL(1,𝔽5)×#624

Splittings

derivedC32×C5 ⋊ C2×C3×C42
HallC33×C5 ⋊ C2×C42
SylowC33 ⋊ C2×C4×AGL(1,𝔽5)
SylowC5 ⋊ C3×C4×#624

Subgroups

subgroupG/H
center, hypercenterC2×C3D32×AGL(1,𝔽5)
commutator, hypocenterC32×C5C2×C3×C42
FrattiniC2C3×D32×AGL(1,𝔽5)
Fitting, socleC2×C33×C5C22×C4
prime radicalC2×C3×D5×C3⋊D3C22
cosocleC2×C32×D5C23×C3
LCSG ▷ C32×C5
UCSC1 ◁ C2×C3

1124 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 120

Conjugacy classes & character table

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

Relationships

maximal subgroup ofD3×AGL(1,𝔽5)×#624, C3×AGL(1,𝔽5)×#3811
maximal normal subgroup ofD3×AGL(1,𝔽5)×#624, C3×AGL(1,𝔽5)×#3811

GAP

Past the SmallGroups library coverage — no SmallGroups id.