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ΓL(1,𝔽16)×C71⋊C7 #44447177

order29820
automorphism?
homologyAbelianization (H1) = C4×C7 · Schur multiplier (H2) = C1

Aliases

direct productΓL(1,𝔽16)×C71⋊C7
unambiguous semidirect productC3⋊(AGL(1,𝔽5)×C71⋊C7)
unambiguous semidirect product(ΓL(1,𝔽16)×C71)⋊C7

Splittings

Fitting, socle, derived, HallC3×C5×C71 ⋊ C4×C7
HallC3×C5×C71⋊C7 ⋊ C4
HallΓL(1,𝔽16)×C71 ⋊ C7
HallC5×C71⋊C7 ⋊ Dic3
HallC3×C71⋊C7 ⋊ AGL(1,𝔽5)
HallC5×C71 ⋊ C7×Dic3
HallC3×C71 ⋊ C7×AGL(1,𝔽5)
SylowC71 ⋊ C7×ΓL(1,𝔽16)
HallC3×C5 ⋊ C4×C71⋊C7
SylowC5 ⋊ Dic3×C71⋊C7
SylowC3 ⋊ AGL(1,𝔽5)×C71⋊C7

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC3×C5×C71C4×C7
prime radicalC3×D5×C71⋊C7C2
cosocleC3×D5×C71C2×C7
LCSG ▷ C3×C5×C71
UCSC1

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1065

Conjugacy classes & character table

153 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29820, 65);