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C2×D3×D5×AGL(1,𝔽5) #72229891

order2400
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC2×D3×D5×AGL(1,𝔽5)

Splittings

Fitting, socleC2×C3×C52 ⋊ C22×C4
derived, HallC3×C52 ⋊ C23×C4
SylowC52 ⋊ C22×C4×D3
SylowC3 ⋊ C22×D5×AGL(1,𝔽5)

Subgroups

subgroupG/H
center, hypercenterC2D3×D5×AGL(1,𝔽5)
commutator, hypocenterC3×C52C23×C4
FrattiniC1G
Fitting, socleC2×C3×C52C22×C4
prime radicalC2×D3×D52C2
cosocleC3×C5×D5C24
LCSG ▷ C3×C52
UCSC1 ◁ C2

976 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 120

Conjugacy classes & character table

120 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×D3×AGL(1,𝔽5)2, D3×D5×C22⋊AGL(1,𝔽5), D3×(C2×AGL(1,𝔽5))⋊AGL(1,𝔽5), …
maximal normal subgroup ofC2×D3×AGL(1,𝔽5)2, D3×D5×C22⋊AGL(1,𝔽5), D3×(C2×AGL(1,𝔽5))⋊AGL(1,𝔽5)
maximal quotient ofD3×D5×C22⋊AGL(1,𝔽5), D3×#11717347, D32×D5×AGL(1,𝔽5), …

GAP

Past the SmallGroups library coverage — no SmallGroups id.