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AGL(1,𝔽7)×D299 #38737355

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

Aliases

direct productAGL(1,𝔽7)×D299
unambiguous semidirect productD7⋊(C3×D299)
unambiguous semidirect product(C13×AGL(1,𝔽7))⋊D23
unambiguous semidirect product(C23×AGL(1,𝔽7))⋊D13

Splittings

Fitting, socle, derived, HallC7×C13×C23 ⋊ C22×C3
HallD7×D299 ⋊ C3
HallC13×ΓL(1,𝔽8)×C23 ⋊ C22
HallΓL(1,𝔽8)×C23 ⋊ C2×D13
HallC13×C23 ⋊ C2×AGL(1,𝔽7)
HallC13×ΓL(1,𝔽8) ⋊ C2×D23
HallC7×C23 ⋊ C2×C3×D13
HallC7×C13 ⋊ C2×C3×D23
SylowC23 ⋊ D13×AGL(1,𝔽7)
HallΓL(1,𝔽8) ⋊ C2×D299
SylowC13 ⋊ AGL(1,𝔽7)×D23
SylowC7 ⋊ C2×C3×D299

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC7×C13×C23C22×C3
LCSG ▷ C7×C13×C23
UCSC1

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2093

Conjugacy classes & character table

1057 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25116, 74);