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ΓL(1,𝔽8)⋊C4×C71⋊C5 #44447159

order29820
automorphism?
homologyAbelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1

Aliases

direct productΓL(1,𝔽8)⋊C4×C71⋊C5
unambiguous semidirect productΓL(1,𝔽8)⋊(C4×C71⋊C5)
unambiguous semidirect productDic7⋊(C3×C71⋊C5)
unambiguous semidirect product(C71×ΓL(1,𝔽8)⋊C4)⋊C5
unambiguous semidirect product(Dic7×C71⋊C5)⋊C3

Splittings

derived, HallC7×C71 ⋊ C3×C4×C5
HallDic7×C71⋊C5 ⋊ C3
HallΓL(1,𝔽8)×C71⋊C5 ⋊ C4
HallC71×ΓL(1,𝔽8)⋊C4 ⋊ C5
HallC7×C71⋊C5 ⋊ C3×C4
HallDic7×C71 ⋊ C3×C5
HallΓL(1,𝔽8)×C71 ⋊ C4×C5
SylowC71 ⋊ C5×ΓL(1,𝔽8)⋊C4
HallDic7 ⋊ C3×C71⋊C5
HallΓL(1,𝔽8) ⋊ C4×C71⋊C5
SylowC7 ⋊ C3×C4×C71⋊C5

Subgroups

subgroupG/H
center, Frattini, hypercenterC2AGL(1,𝔽7)×C71⋊C5
commutator, hypocenterC7×C71C3×C4×C5
Fitting, socle, cosocleC2×C7×C71C2×C3×C5
prime radicalC2×ΓL(1,𝔽8)×C71⋊C5C2
LCSG ▷ C7×C71
UCSC1 ◁ C2

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1988

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29820, 47);