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C2×D3×AGL(1,𝔽5)×AGL(1,𝔽7) #72217399

order10080
automorphism?
homologyAbelianization (H1) = C23×C3×C4 · Schur multiplier (H2) = C26

Aliases

direct productC2×D3×AGL(1,𝔽5)×AGL(1,𝔽7)

Splittings

Fitting, socleC2×C3×C5×C7 ⋊ C22×C3×C4
derivedC3×C5×C7 ⋊ C23×C3×C4
HallC3×C5×ΓL(1,𝔽8) ⋊ C23×C4
HallC3×ΓL(1,𝔽8) ⋊ C23×AGL(1,𝔽5)
HallC5×C7 ⋊ C22×C3×C4×D3
SylowC7 ⋊ C22×C3×D3×AGL(1,𝔽5)
SylowC5 ⋊ C2×C4×D3×AGL(1,𝔽7)

Subgroups

subgroupG/H
center, hypercenterC2D3×AGL(1,𝔽5)×AGL(1,𝔽7)
commutator, hypocenterC3×C5×C7C23×C3×C4
FrattiniC1G
Fitting, socleC2×C3×C5×C7C22×C3×C4
prime radicalC2×D3×D5×AGL(1,𝔽7)C2
cosocleC3×C7×D5C24×C3
LCSG ▷ C3×C5×C7
UCSC1 ◁ C2

1996 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

210 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD32×AGL(1,𝔽5)×AGL(1,𝔽7)
maximal quotient ofD32×AGL(1,𝔽5)×AGL(1,𝔽7)
automorphism group ofC3×D7×D15, C3×D5×D21, C3×D3×D35, …
holomorph ofC2×C3×C5×C7

GAP

Past the SmallGroups library coverage — no SmallGroups id.