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D4×D5×3−1+2 #72247373

order2160
automorphism?
homologyAbelianization (H1) = C23×C32 · Schur multiplier (H2) = C23

Aliases

direct productD4×D5×3−1+2

Splittings

FittingC5×D4×3−1+2 ⋊ C2
HallC5×3−1+2 ⋊ C2×D4
SylowC5 ⋊ C2×D4×3−1+2

Subgroups

subgroupG/H
center, FrattiniC2×C3C22×C32×D5
commutator, socle, cosocleC2×C3×C5C23×C32
FittingC5×D4×3−1+2C2
prime radicalC32×D4×D5C3
hypercenterD4×3−1+2D5
hypocenterC5C2×D4×3−1+2
LCSG ▷ C2×C3×C5 ▷ C5
UCSC1 ◁ C2×C3 ◁ D4×3−1+2

432 conjugacy classes of subgroups; only the 175 normal subgroups are shown.

normal subgroups only

This group has 432 conjugacy classes of subgroups — too many to draw. Only its 175 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

transitive degreeμt(G) = 180

Conjugacy classes & character table

220 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD4×AGL(1,𝔽5)×3−1+2, D4×D5×AGL(1,ℤ/9), D4×3−1+2⋊AGL(1,𝔽5), …
maximal normal subgroup ofD4×AGL(1,𝔽5)×3−1+2, D4×D5×AGL(1,ℤ/9), D4×3−1+2⋊AGL(1,𝔽5)
maximal quotient of3−1+2×#87886

GAP

Past the SmallGroups library coverage — no SmallGroups id.