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D4×AGL(1,𝔽5)×3−1+2 #72247384

order4320
automorphism?
homologyAbelianization (H1) = C22×C32×C4 · Schur multiplier (H2) = C23

Aliases

direct productD4×AGL(1,𝔽5)×3−1+2

Splittings

FittingC5×D4×3−1+2 ⋊ C4
HallC5×3−1+2 ⋊ C4×D4
SylowC5 ⋊ C4×D4×3−1+2

Subgroups

subgroupG/H
center, FrattiniC2×C3C22×C32×AGL(1,𝔽5)
commutator, socleC2×C3×C5C22×C32×C4
FittingC5×D4×3−1+2C4
prime radicalC32×D4×D5C2×C3
cosocleC2×C3×D5C23×C32
hypercenterD4×3−1+2AGL(1,𝔽5)
hypocenterC5C4×D4×3−1+2
LCSG ▷ C2×C3×C5 ▷ C5
UCSC1 ◁ C2×C3 ◁ D4×3−1+2

752 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 180

Conjugacy classes & character table

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

Relationships

maximal subgroup ofD4×AGL(1,𝔽5)×AGL(1,ℤ/9), AGL(1,𝔽5)×S4×3−1+2, 3−1+2×#11717375
maximal normal subgroup ofD4×AGL(1,𝔽5)×AGL(1,ℤ/9)
maximal quotient of3−1+2×#11717375

GAP

Past the SmallGroups library coverage — no SmallGroups id.