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C23×(C31⋊C3)⋊C5 #72219346

order3720
isoclinismisoclinic class of (C31⋊C3)⋊C5
automorphism?
homologyAbelianization (H1) = C23×C3×C5 · Schur multiplier (H2) = C23

Aliases

direct productC23×(C31⋊C3)⋊C5

Splittings

Fitting, socle, HallC23×C31 ⋊ C3×C5
derived, SylowC31 ⋊ C23×C3×C5
HallC23×ΓL(1,𝔽32) ⋊ C3
HallC23×C31⋊C3 ⋊ C5
HallΓL(1,𝔽32) ⋊ C23×C3
HallC31⋊C3 ⋊ C23×C5

Subgroups

subgroupG/H
center, hypercenterC23(C31⋊C3)⋊C5
commutator, cosocle, hypocenterC31C23×C3×C5
FrattiniC1G
Fitting, socleC23×C31C3×C5
LCSG ▷ C31
UCSC1 ◁ C23

128 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

136 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC22×D3×(C31⋊C3)⋊C5, C23×AGL(1,𝔽31), C22×C4×(C31⋊C3)⋊C5, …
maximal normal subgroup ofC23×AGL(1,𝔽31), C22×C4×(C31⋊C3)⋊C5, C22×((C31⋊C3)⋊C4)⋊C5, …
maximal quotient ofC22×D3×(C31⋊C3)⋊C5, C22×C4×(C31⋊C3)⋊C5, C2×D4×(C31⋊C3)⋊C5

GAP

Past the SmallGroups library coverage — no SmallGroups id.