Finite Group Databasebeta

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C19×ΓL(1,𝔽8)×#595 #41029520

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

Aliases

direct productC19×ΓL(1,𝔽8)×#595
unambiguous semidirect product(C7×#595)⋊(C3×C19)

Splittings

Fitting, socle, HallC7×C17×C19 ⋊ C3×C4
derived, HallC7×C17 ⋊ C3×C4×C19
HallC7×C19×#595 ⋊ C3
HallC17×C19×ΓL(1,𝔽8) ⋊ C4
HallC7×#595 ⋊ C3×C19
HallC17×ΓL(1,𝔽8) ⋊ C4×C19
HallC17×C19 ⋊ C4×ΓL(1,𝔽8)
HallC7×C19 ⋊ C3×#595
SylowC17 ⋊ C4×C19×ΓL(1,𝔽8)
SylowC7 ⋊ C3×C19×#595

Subgroups

subgroupG/H
center, hypercenterC19ΓL(1,𝔽8)×#595
commutator, hypocenterC7×C17C3×C4×C19
FrattiniC1G
Fitting, socleC7×C17×C19C3×C4
prime radicalC19×ΓL(1,𝔽8)×D17C2
cosocleC7×D17C2×C3×C19
LCSG ▷ C7×C17
UCSC1 ◁ C19

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2261

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(27132, 77);