Finite Group Databasebeta

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C22×3−1+2×C5⋊D5 #72247338

order5400
automorphism?
homologyAbelianization (H1) = C23×C32 · Schur multiplier (H2) = C23×C5

Aliases

direct productC22×3−1+2×C5⋊D5

Splittings

FittingC22×C52×3−1+2 ⋊ C2
HallC52×3−1+2 ⋊ C23
SylowC52 ⋊ C23×3−1+2

Subgroups

subgroupG/H
centerC22×C3C32×C5⋊D5
commutator, cosocleC3×C52C23×C32
FrattiniC3C22×C32×C5⋊D5
FittingC22×C52×3−1+2C2
socleC22×C3×C52C2×C32
prime radicalC22×C32×C5⋊D5C3
hypercenterC22×3−1+2C5⋊D5
hypocenterC52C23×3−1+2
LCSG ▷ C3×C52 ▷ C52
UCSC1 ◁ C22×C3 ◁ C22×3−1+2

1024 conjugacy classes of subgroups; only the 357 normal subgroups are shown.

normal subgroups only

This group has 1024 conjugacy classes of subgroups — too many to draw. Only its 357 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) = 900

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC22×3−1+2×#1043, C22×C5⋊D5×AGL(1,ℤ/9), C22×#72222340, …
maximal normal subgroup ofC22×3−1+2×#1043, C22×C5⋊D5×AGL(1,ℤ/9), C22×#72222340, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.