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C23×#11763984 #38737337

order25116
automorphism?
homologyAbelianization (H1) = C3×C4×C23 · Schur multiplier (H2) = C1

Aliases

direct productC23×#11763984

Splittings

Fitting, socle, HallC7×C13×C23 ⋊ C3×C4
derived, HallC7×C13 ⋊ C3×C4×C23
HallC23×C7⋊#261 ⋊ C3
HallC23×#63271 ⋊ C4
HallC7⋊#261 ⋊ C3×C23
HallC13×C23 ⋊ ΓL(1,𝔽8)⋊C4
Hall#63271 ⋊ C4×C23
HallC7×C23 ⋊ AGL(1,𝔽13)
SylowC13 ⋊ C23×ΓL(1,𝔽8)⋊C4
SylowC7 ⋊ C23×AGL(1,𝔽13)

Subgroups

subgroupG/H
center, hypercenterC23#11763984
commutator, hypocenterC7×C13C3×C4×C23
FrattiniC1G
Fitting, socleC7×C13×C23C3×C4
prime radicalC23×#10587717C2
cosocleC7×D13C2×C3×C23
LCSG ▷ C7×C13
UCSC1 ◁ C23

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2093

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25116, 56);