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C107×C5⋊AGL(1,𝔽7) #36376432

order22470
automorphism?
homologyAbelianization (H1) = C2×C3×C107 · Schur multiplier (H2) = C1

Aliases

direct productC107×C5⋊AGL(1,𝔽7)
unambiguous semidirect productC5⋊(AGL(1,𝔽7)×C107)
unambiguous semidirect productΓL(1,𝔽8)⋊(D5×C107)
unambiguous semidirect productD35⋊(C3×C107)
unambiguous semidirect product(D35×C107)⋊C3

Splittings

Fitting, socle, HallC5×C7×C107 ⋊ C2×C3
derived, HallC5×C7 ⋊ C2×C3×C107
HallC5×ΓL(1,𝔽8)×C107 ⋊ C2
HallD35×C107 ⋊ C3
HallΓL(1,𝔽8)×C107 ⋊ D5
HallC7×C107 ⋊ C3×D5
HallC5×C107 ⋊ AGL(1,𝔽7)
HallC5×ΓL(1,𝔽8) ⋊ C2×C107
HallD35 ⋊ C3×C107
HallΓL(1,𝔽8) ⋊ D5×C107
SylowC7 ⋊ C3×D5×C107
SylowC5 ⋊ AGL(1,𝔽7)×C107

Subgroups

subgroupG/H
center, hypercenterC107C5⋊AGL(1,𝔽7)
commutator, cosocle, hypocenterC5×C7C2×C3×C107
FrattiniC1G
Fitting, socleC5×C7×C107C2×C3
LCSG ▷ C5×C7
UCSC1 ◁ C107

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3745

Conjugacy classes & character table

1819 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22470, 23);