Finite Group Databasebeta

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C2×C3×C5×GO+(4,𝔽2) #72217474

order2160
isoclinismisoclinic class of GO+(4,𝔽2)
automorphism?
homologyAbelianization (H1) = C23×C3×C5 · Schur multiplier (H2) = C23

Aliases

direct productC2×C3×C5×GO+(4,𝔽2)

Splittings

Fitting, socleC2×C33×C5 ⋊ D4
HallC33×C5 ⋊ C2×D4
SylowC33 ⋊ C2×C5×D4

Subgroups

subgroupG/H
center, hypercenterC2×C3×C5GO+(4,𝔽2)
commutator, cosocleC3⋊D3C23×C3×C5
FrattiniC1G
Fitting, socleC2×C33×C5D4
hypocenterC32C2×C3×C5×D4
LCSG ▷ C3⋊D3 ▷ C32
UCSC1 ◁ C2×C3×C5

384 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 384 conjugacy classes of subgroups — too many to draw. Only its 84 normal subgroups are shown.

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

Full subgroup data →

Conjugacy classes & character table

270 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C3×D5×GO+(4,𝔽2), C2×C3×C5×AΓL(1,𝔽9), C2×C3×#10624311, …
maximal normal subgroup ofC2×C3×D5×GO+(4,𝔽2), C2×C3×C5×AΓL(1,𝔽9), C2×C3×#10624311, …
maximal quotient ofC22×C3×C5×GO+(4,𝔽2), C3×C4×C5×GO+(4,𝔽2)

GAP

Past the SmallGroups library coverage — no SmallGroups id.