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C2×((C31⋊C3)⋊C4)⋊C5 #72219331

order3720
automorphism?
homologyAbelianization (H1) = C2×C3×C4×C5 · Schur multiplier (H2) = C2

Aliases

direct productC2×((C31⋊C3)⋊C4)⋊C5

Splittings

derived, SylowC31 ⋊ C2×C3×C4×C5
HallC2×Dic31⋊C5 ⋊ C3
HallC2×(C31⋊C3)⋊C4 ⋊ C5
Hall(C31⋊C3)⋊C5 ⋊ C2×C4
HallC2×Dic31 ⋊ C3×C5
HallΓL(1,𝔽32) ⋊ C2×C3×C4
HallC31⋊C3 ⋊ C2×C4×C5

Subgroups

subgroupG/H
center, hypercenterC22AGL(1,𝔽31)
commutator, hypocenterC31C2×C3×C4×C5
FrattiniC2C2×AGL(1,𝔽31)
Fitting, socleC22×C31C2×C3×C5
prime radicalC22×(C31⋊C3)⋊C5C2
cosocleC2×C31C22×C3×C5
LCSG ▷ C31
UCSC1 ◁ C22

64 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

124 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×((C31⋊C3)⋊C4)⋊C5, C2×C3×((C31⋊C3)⋊C4)⋊C5, C2×C3⋊(((C31⋊C3)⋊C4)⋊C5), …
maximal normal subgroup ofC2×C3×((C31⋊C3)⋊C4)⋊C5, C2×C4×AGL(1,𝔽31), C22×((C31⋊C3)⋊C4)⋊C5, …
maximal quotient ofD3×((C31⋊C3)⋊C4)⋊C5, C2×C3×((C31⋊C3)⋊C4)⋊C5, C2×C3⋊(((C31⋊C3)⋊C4)⋊C5), …

GAP

Past the SmallGroups library coverage — no SmallGroups id.