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D5×ΓL(1,𝔽8)×C53 #26013287

order11130
automorphism?
homologyAbelianization (H1) = C2×C3×C53 · Schur multiplier (H2) = C1

Aliases

direct productD5×ΓL(1,𝔽8)×C53
unambiguous semidirect productC5⋊(C2×ΓL(1,𝔽8)×C53)
unambiguous semidirect product(C7×D5)⋊(C3×C53)
unambiguous semidirect product(C7×D5×C53)⋊C3

Splittings

Fitting, socle, HallC5×C7×C53 ⋊ C2×C3
derived, HallC5×C7 ⋊ C2×C3×C53
HallC5×ΓL(1,𝔽8)×C53 ⋊ C2
HallC7×D5×C53 ⋊ C3
HallC7×C53 ⋊ C3×D5
HallC5×C53 ⋊ C2×ΓL(1,𝔽8)
HallC5×ΓL(1,𝔽8) ⋊ C2×C53
HallC7×D5 ⋊ C3×C53
SylowC7 ⋊ C3×D5×C53
SylowC5 ⋊ C2×ΓL(1,𝔽8)×C53

Subgroups

subgroupG/H
center, hypercenterC53D5×ΓL(1,𝔽8)
commutator, cosocle, hypocenterC5×C7C2×C3×C53
FrattiniC1G
Fitting, socleC5×C7×C53C2×C3
LCSG ▷ C5×C7
UCSC1 ◁ C53

32 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1060 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC53×ΓL(1,𝔽8)⋊AGL(1,𝔽5), ΓL(1,𝔽8)⋊#11761507, AGL(1,𝔽5)×ΓL(1,𝔽8)×C53, …
maximal normal subgroup ofC53×ΓL(1,𝔽8)⋊AGL(1,𝔽5), ΓL(1,𝔽8)⋊#11761507, AGL(1,𝔽5)×ΓL(1,𝔽8)×C53, …
maximal quotient ofDic5×ΓL(1,𝔽8)×C53, C2×D5×ΓL(1,𝔽8)×C53, D5×C53×C7⋊C9, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11130, 21);