Finite Group Databasebeta

← Prev (#36348996) Next (#36348998) →

C17×ΓL(1,𝔽8)×D31 #36348997

order22134
automorphism?
homologyAbelianization (H1) = C2×C3×C17 · Schur multiplier (H2) = C1

Aliases

direct productC17×ΓL(1,𝔽8)×D31

Splittings

Fitting, socle, HallC7×C17×C31 ⋊ C2×C3
derived, HallC7×C31 ⋊ C2×C3×C17
HallC17×ΓL(1,𝔽8)×C31 ⋊ C2
HallC7×C17×D31 ⋊ C3
HallΓL(1,𝔽8)×C31 ⋊ C2×C17
HallC17×C31 ⋊ C2×ΓL(1,𝔽8)
HallC7×D31 ⋊ C3×C17
HallC7×C17 ⋊ C3×D31
SylowC31 ⋊ C2×C17×ΓL(1,𝔽8)
SylowC7 ⋊ C3×C17×D31

Subgroups

subgroupG/H
center, hypercenterC17ΓL(1,𝔽8)×D31
commutator, cosocle, hypocenterC7×C31C2×C3×C17
FrattiniC1G
Fitting, socleC7×C17×C31C2×C3
LCSG ▷ C7×C31
UCSC1 ◁ C17

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3689

Conjugacy classes & character table

1445 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22134, 22);