Finite Group Databasebeta

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C3×C7⋊(D131⋊C5) #42118024

order27510
automorphism?
homologyAbelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1

Aliases

direct productC3×C7⋊(D131⋊C5)
unambiguous semidirect product(C131⋊C5)⋊(C3×D7)
unambiguous semidirect product(C3×D917)⋊C5

Splittings

Fitting, socle, HallC3×C7×C131 ⋊ C2×C5
derived, HallC7×C131 ⋊ C2×C3×C5
HallC3×C7×C131⋊C5 ⋊ C2
HallC3×D917 ⋊ C5
HallC7×C131⋊C5 ⋊ C2×C3
HallC3×C131⋊C5 ⋊ D7
HallD917 ⋊ C3×C5
HallC131⋊C5 ⋊ C3×D7
HallC3×C131 ⋊ C5×D7
SylowC131 ⋊ C3×C5×D7
HallC3×C7 ⋊ D131⋊C5
SylowC7 ⋊ C3×D131⋊C5

Subgroups

subgroupG/H
center, hypercenterC3C7⋊(D131⋊C5)
commutator, cosocle, hypocenterC7×C131C2×C3×C5
FrattiniC1G
Fitting, socleC3×C7×C131C2×C5
LCSG ▷ C7×C131
UCSC1 ◁ C3

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2751

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(27510, 22);