Finite Group Databasebeta

← Prev (#23748883) Next (#23748885) →

C3×ΓL(1,𝔽8)×C151 #23748884

order9513
isoclinismisoclinic class of ΓL(1,𝔽8)
automorphism?
homologyAbelianization (H1) = C32×C151 · Schur multiplier (H2) = C3

Aliases

direct productC3×ΓL(1,𝔽8)×C151
unambiguous semidirect productC7⋊(C32×C151)
unambiguous semidirect product(C3×C7)⋊(C3×C151)

Splittings

Fitting, socleC3×C7×C151 ⋊ C3
derived, SylowC7 ⋊ C32×C151
HallC7×C151 ⋊ C32

Subgroups

subgroupG/H
center, hypercenterC3×C151ΓL(1,𝔽8)
commutator, cosocle, hypocenterC7C32×C151
FrattiniC1G
Fitting, socleC3×C7×C151C3
LCSG ▷ C7
UCSC1 ◁ C3×C151

24 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2265 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC3×AGL(1,𝔽7)×C151, C3×ΓL(1,𝔽8)⋊D151, C3×ΓL(1,𝔽8)×D151, …
maximal normal subgroup ofC3×AGL(1,𝔽7)×C151, C3×ΓL(1,𝔽8)⋊D151, C3×ΓL(1,𝔽8)×D151, …
maximal quotient ofC2×C3×ΓL(1,𝔽8)×C151, A4×ΓL(1,𝔽8)×C151, C3×C22⋊ΓL(1,𝔽8)×C151

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9513, 10);