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C2×C23⋊#10587717 #38737394

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

Aliases

direct productC2×C23⋊#10587717
unambiguous semidirect product(C2×C23)⋊#10587717

Splittings

Fitting, socleC2×C7×C13×C23 ⋊ C2×C3
derived, HallC7×C13×C23 ⋊ C22×C3
HallC2×C7×D299 ⋊ C3
HallC23×#63271 ⋊ C22
HallC2×D299 ⋊ ΓL(1,𝔽8)
HallC13×C23 ⋊ C22×ΓL(1,𝔽8)
Hall#63271 ⋊ C2×D23
HallC7×C23 ⋊ C2×D13⋊C3
HallC7×C13 ⋊ C2×C3×D23
SylowC23 ⋊ C2×#10587717
SylowC13 ⋊ C2×ΓL(1,𝔽8)×D23
SylowC7 ⋊ C2×C23⋊(D13⋊C3)

Subgroups

subgroupG/H
center, hypercenterC2C23⋊#10587717
commutator, cosocle, hypocenterC7×C13×C23C22×C3
FrattiniC1G
Fitting, socleC2×C7×C13×C23C2×C3
LCSG ▷ C7×C13×C23
UCSC1 ◁ C2

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4186

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25116, 113);