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C2×D23×#63271 #38737396

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

Aliases

direct productC2×D23×#63271
unambiguous semidirect productC23⋊(C22×#63271)
unambiguous semidirect product(C2×C23)⋊(C2×#63271)

Splittings

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

Subgroups

subgroupG/H
center, hypercenterC2D23×#63271
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

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25116, 115);