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C2×C13×C23×AGL(1,𝔽7) #38737378

order25116
automorphism?
homologyAbelianization (H1) = C22×C3×C13×C23 · Schur multiplier (H2) = C2

Aliases

direct productC2×C13×C23×AGL(1,𝔽7)
unambiguous semidirect productD7⋊(C2×C3×C13×C23)
unambiguous semidirect productΓL(1,𝔽8)⋊(C22×C13×C23)
unambiguous semidirect product(C2×D7)⋊(C3×C13×C23)
unambiguous semidirect product(C2×ΓL(1,𝔽8))⋊(C2×C13×C23)
unambiguous semidirect product(C2×D7×C23)⋊(C3×C13)

Splittings

Fitting, socleC2×C7×C13×C23 ⋊ C2×C3
derived, SylowC7 ⋊ C22×C3×C13×C23
HallC2×C13×D7×C23 ⋊ C3
HallC13×ΓL(1,𝔽8)×C23 ⋊ C22
HallC7×C13×C23 ⋊ C22×C3
HallC2×D7×C23 ⋊ C3×C13
HallΓL(1,𝔽8)×C23 ⋊ C22×C13
HallC2×C13×D7 ⋊ C3×C23
HallC13×ΓL(1,𝔽8) ⋊ C22×C23
HallC7×C23 ⋊ C22×C3×C13
HallC7×C13 ⋊ C22×C3×C23
HallC2×D7 ⋊ C3×C13×C23
HallΓL(1,𝔽8) ⋊ C22×C13×C23

Subgroups

subgroupG/H
center, hypercenterC2×C13×C23AGL(1,𝔽7)
commutator, cosocle, hypocenterC7C22×C3×C13×C23
FrattiniC1G
Fitting, socleC2×C7×C13×C23C2×C3
LCSG ▷ C7
UCSC1 ◁ C2×C13×C23

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4186

Conjugacy classes & character table

4186 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25116, 97);