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C22×ΓL(1,𝔽8)×C71⋊C5 #44447193

order29820
automorphism?
homologyAbelianization (H1) = C22×C3×C5 · Schur multiplier (H2) = C2

Aliases

direct productC22×ΓL(1,𝔽8)×C71⋊C5
unambiguous semidirect product(C22×ΓL(1,𝔽8)×C71)⋊C5

Splittings

Fitting, socle, HallC22×C7×C71 ⋊ C3×C5
derived, HallC7×C71 ⋊ C22×C3×C5
HallC22×C7×C71⋊C5 ⋊ C3
HallC22×ΓL(1,𝔽8)×C71 ⋊ C5
HallC7×C71⋊C5 ⋊ C22×C3
HallΓL(1,𝔽8)×C71 ⋊ C22×C5
HallC22×C71 ⋊ C5×ΓL(1,𝔽8)
SylowC71 ⋊ C22×C5×ΓL(1,𝔽8)
HallC22×C7 ⋊ C3×C71⋊C5
SylowC7 ⋊ C22×C3×C71⋊C5

Subgroups

subgroupG/H
center, hypercenterC22ΓL(1,𝔽8)×C71⋊C5
commutator, cosocle, hypocenterC7×C71C22×C3×C5
FrattiniC1G
Fitting, socleC22×C7×C71C3×C5
LCSG ▷ C7×C71
UCSC1 ◁ C22

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1988

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29820, 81);