Finite Group Databasebeta

← Prev (#22575572) Next (#22575574) →

D5×ΓL(1,𝔽8)×C41 #22575573

order8610
automorphism?
homologyAbelianization (H1) = C2×C3×C41 · Schur multiplier (H2) = C1

Aliases

direct productD5×ΓL(1,𝔽8)×C41
unambiguous semidirect productC5⋊(C2×ΓL(1,𝔽8)×C41)
unambiguous semidirect product(C7×D5)⋊(C3×C41)
unambiguous semidirect product(C7×D5×C41)⋊C3

Splittings

Fitting, socle, HallC5×C7×C41 ⋊ C2×C3
derived, HallC5×C7 ⋊ C2×C3×C41
HallC5×ΓL(1,𝔽8)×C41 ⋊ C2
HallC7×D5×C41 ⋊ C3
HallC7×C41 ⋊ C3×D5
HallC5×C41 ⋊ C2×ΓL(1,𝔽8)
HallC5×ΓL(1,𝔽8) ⋊ C2×C41
HallC7×D5 ⋊ C3×C41
SylowC7 ⋊ C3×D5×C41
SylowC5 ⋊ C2×ΓL(1,𝔽8)×C41

Subgroups

subgroupG/H
center, hypercenterC41D5×ΓL(1,𝔽8)
commutator, hypocenterC5×C7C2×C3×C41
FrattiniC1G
Fitting, socleC5×C7×C41C2×C3
LCSG ▷ C5×C7
UCSC1 ◁ C41

32 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

820 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC41×ΓL(1,𝔽8)⋊AGL(1,𝔽5), ΓL(1,𝔽8)⋊#11717963, AGL(1,𝔽5)×ΓL(1,𝔽8)×C41, …
maximal normal subgroup ofC41×ΓL(1,𝔽8)⋊AGL(1,𝔽5), ΓL(1,𝔽8)⋊#11717963, AGL(1,𝔽5)×ΓL(1,𝔽8)×C41, …
maximal quotient ofDic5×ΓL(1,𝔽8)×C41, C2×D5×ΓL(1,𝔽8)×C41, D5×C41×C7⋊C9, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8610, 30);