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C2×C7×C13⋊C3×D23 #38737377

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

Aliases

direct productC2×C7×C13⋊C3×D23
unambiguous semidirect productC23⋊(C22×C7×C13⋊C3)
unambiguous semidirect product(C2×C23)⋊(C2×C7×C13⋊C3)
unambiguous semidirect product(C2×C13×D23)⋊(C3×C7)

Splittings

Fitting, socleC2×C7×C13×C23 ⋊ C2×C3
derived, HallC13×C23 ⋊ C22×C3×C7
HallC2×C7×C13×D23 ⋊ C3
HallC7×C23×C13⋊C3 ⋊ C22
HallC7×C13×C23 ⋊ C22×C3
HallC2×C13×D23 ⋊ C3×C7
HallC23×C13⋊C3 ⋊ C22×C7
HallC7×C23 ⋊ C22×C13⋊C3
HallC7×C13 ⋊ C2×C3×D23
SylowC23 ⋊ C22×C7×C13⋊C3
SylowC13 ⋊ C2×C3×C7×D23

Subgroups

subgroupG/H
center, hypercenterC2×C7C13⋊C3×D23
commutator, cosocle, hypocenterC13×C23C22×C3×C7
FrattiniC1G
Fitting, socleC2×C7×C13×C23C2×C3
LCSG ▷ C13×C23
UCSC1 ◁ C2×C7

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4186

Conjugacy classes & character table

1274 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25116, 96);