Finite Group Databasebeta

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3−1+2×#87886 #72254649

order10800
automorphism?
homologyAbelianization (H1) = C23×C32 · Schur multiplier (H2) = C23

Aliases

direct product3−1+2×#87886

Splittings

FittingC22×C52×3−1+2 ⋊ C22
HallC52×3−1+2 ⋊ C2×D4
SylowC52 ⋊ C2×D4×3−1+2

Subgroups

subgroupG/H
center, FrattiniC2×C3C2×C32×D52
commutator, socle, cosocleC2×C3×C52C23×C32
FittingC22×C52×3−1+2C22
prime radicalC32×#87886C3
hypercenterC22×3−1+2D52
hypocenterC52C2×D4×3−1+2
LCSG ▷ C2×C3×C52 ▷ C52
UCSC1 ◁ C2×C3 ◁ C22×3−1+2

1120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 180

Conjugacy classes & character table

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

Relationships

maximal subgroup of3−1+2×#11717375, AGL(1,ℤ/9)×#87886, #72254787
maximal normal subgroup of3−1+2×#11717375, AGL(1,ℤ/9)×#87886, #72254787

GAP

Past the SmallGroups library coverage — no SmallGroups id.