Finite Group Databasebeta

← Prev (#41029476) Next (#41029478) →

C17×C19×ΓL(1,𝔽8)⋊C4 #41029477

order27132
automorphism?
homologyAbelianization (H1) = C3×C4×C17×C19 · Schur multiplier (H2) = C1

Aliases

direct productC17×C19×ΓL(1,𝔽8)⋊C4
unambiguous semidirect productΓL(1,𝔽8)⋊(C4×C17×C19)
unambiguous semidirect productDic7⋊(C3×C17×C19)
unambiguous semidirect product(C17×Dic7)⋊(C3×C19)

Splittings

derived, SylowC7 ⋊ C3×C4×C17×C19
HallC17×C19×Dic7 ⋊ C3
HallC17×C19×ΓL(1,𝔽8) ⋊ C4
HallC7×C17×C19 ⋊ C3×C4
HallC19×Dic7 ⋊ C3×C17
HallC17×Dic7 ⋊ C3×C19
HallC19×ΓL(1,𝔽8) ⋊ C4×C17
HallC17×ΓL(1,𝔽8) ⋊ C4×C19
HallC7×C19 ⋊ C3×C4×C17
HallC7×C17 ⋊ C3×C4×C19
HallDic7 ⋊ C3×C17×C19
HallΓL(1,𝔽8) ⋊ C4×C17×C19

Subgroups

subgroupG/H
center, hypercenterC2×C17×C19AGL(1,𝔽7)
commutator, hypocenterC7C3×C4×C17×C19
FrattiniC2C17×C19×AGL(1,𝔽7)
Fitting, socleC2×C7×C17×C19C2×C3
prime radicalC2×C17×C19×ΓL(1,𝔽8)C2
cosocleC2×C7C2×C3×C17×C19
LCSG ▷ C7
UCSC1 ◁ C2×C17×C19

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9044

Conjugacy classes & character table

4522 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(27132, 34);