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C7×D23×D13⋊C3 #38737333

order25116
automorphism?
homologyAbelianization (H1) = C22×C3×C7 · Schur multiplier (H2) = C2

Aliases

direct productC7×D23×D13⋊C3
unambiguous semidirect productD13⋊(C3×C7×D23)
unambiguous semidirect product(D13×D23)⋊(C3×C7)
unambiguous semidirect product(C13⋊C3×D23)⋊(C2×C7)
unambiguous semidirect product(C23×D13⋊C3)⋊(C2×C7)
unambiguous semidirect product(C23⋊(D13⋊C3))⋊(C2×C7)

Splittings

Fitting, socle, HallC7×C13×C23 ⋊ C22×C3
derived, HallC13×C23 ⋊ C22×C3×C7
HallC7×D13×D23 ⋊ C3
HallC7×C23×C13⋊C3 ⋊ C22
HallD13×D23 ⋊ C3×C7
HallC23×C13⋊C3 ⋊ C22×C7
HallC7×C13⋊C3 ⋊ C2×D23
HallC7×C23 ⋊ C2×D13⋊C3
HallC7×C13 ⋊ C2×C3×D23
HallC13⋊C3 ⋊ C2×C7×D23
SylowC23 ⋊ C2×C7×D13⋊C3
SylowC13 ⋊ C2×C3×C7×D23

Subgroups

subgroupG/H
center, hypercenterC7D23×D13⋊C3
commutator, cosocle, hypocenterC13×C23C22×C3×C7
FrattiniC1G
Fitting, socleC7×C13×C23C22×C3
LCSG ▷ C13×C23
UCSC1 ◁ C7

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2093

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25116, 52);