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C5×AGL(1,𝔽7)×C109 #37504341

order22890
automorphism?
homologyAbelianization (H1) = C2×C3×C5×C109 · Schur multiplier (H2) = C1

Aliases

direct productC5×AGL(1,𝔽7)×C109
unambiguous semidirect productD7⋊(C3×C5×C109)
unambiguous semidirect productΓL(1,𝔽8)⋊(C2×C5×C109)
unambiguous semidirect product(C5×D7)⋊(C3×C109)

Splittings

Fitting, socle, HallC5×C7×C109 ⋊ C2×C3
derived, SylowC7 ⋊ C2×C3×C5×C109
HallC5×ΓL(1,𝔽8)×C109 ⋊ C2
HallC5×D7×C109 ⋊ C3
HallΓL(1,𝔽8)×C109 ⋊ C2×C5
HallD7×C109 ⋊ C3×C5
HallC7×C109 ⋊ C2×C3×C5
HallC5×ΓL(1,𝔽8) ⋊ C2×C109
HallC5×D7 ⋊ C3×C109
HallC5×C7 ⋊ C2×C3×C109
HallΓL(1,𝔽8) ⋊ C2×C5×C109
HallD7 ⋊ C3×C5×C109

Subgroups

subgroupG/H
center, hypercenterC5×C109AGL(1,𝔽7)
commutator, cosocle, hypocenterC7C2×C3×C5×C109
FrattiniC1G
Fitting, socleC5×C7×C109C2×C3
LCSG ▷ C7
UCSC1 ◁ C5×C109

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3815

Conjugacy classes & character table

3815 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22890, 26);