Finite Group Databasebeta

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3−1+2×#11717375 #72254683

order21600
automorphism?
homologyAbelianization (H1) = C22×C32×C4 · Schur multiplier (H2) = C23

Aliases

direct product3−1+2×#11717375

Splittings

FittingC22×C52×3−1+2 ⋊ C2×C4
HallC52×3−1+2 ⋊ C4×D4
SylowC52 ⋊ C4×D4×3−1+2

Subgroups

subgroupG/H
center, FrattiniC2×C3C2×C32×D5⋊AGL(1,𝔽5)
commutator, socleC2×C3×C52C22×C32×C4
FittingC22×C52×3−1+2C2×C4
prime radicalC32×#87886C2×C3
cosocleC2×C3×C5⋊D5C23×C32
hypercenterC22×3−1+2D5⋊AGL(1,𝔽5)
hypocenterC52C4×D4×3−1+2
LCSG ▷ C2×C3×C52 ▷ C52
UCSC1 ◁ C2×C3 ◁ C22×3−1+2

1936 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 180

Conjugacy classes & character table

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

Relationships

maximal subgroup ofAGL(1,ℤ/9)×#11717375
maximal normal subgroup ofAGL(1,ℤ/9)×#11717375

GAP

Past the SmallGroups library coverage — no SmallGroups id.