Finite Group Databasebeta

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#940×#1043 #72231062

order9600
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25×C4

Aliases

direct product#940×#1043

Splittings

FittingC2×C3×C52×D4 ⋊ C2×C4
HallC3×C52 ⋊ C4×#127
SylowC52 ⋊ C4×#940
SylowC3 ⋊ #127×#1043

Subgroups

subgroupG/H
center, FrattiniC22C22×D3×#1043
commutator, socleC22×C3×C52C23×C4
FittingC2×C3×C52×D4C2×C4
prime radicalC5⋊D5×#940C2
cosocleC22×C3×C5⋊D5C24
hypercenterC2×D4D3×#1043
hypocenterC3×C52C4×#127
LCSG ▷ C22×C3×C52 ▷ C3×C52
UCSC1 ◁ C22 ◁ C2×D4

7392 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1200

Conjugacy classes & character table

240 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×#127×#1043
maximal normal subgroup ofD3×#127×#1043

GAP

Past the SmallGroups library coverage — no SmallGroups id.