Finite Group Databasebeta

← Prev (#31798226) Next (#31798228) →

C19×C11⋊(ΓL(1,𝔽8)⋊C4) #31798227

order17556
automorphism?
homologyAbelianization (H1) = C3×C4×C19 · Schur multiplier (H2) = C1

Aliases

direct productC19×C11⋊(ΓL(1,𝔽8)⋊C4)
unambiguous semidirect productC11⋊(C19×ΓL(1,𝔽8)⋊C4)
unambiguous semidirect productΓL(1,𝔽8)⋊(C19×Dic11)
unambiguous semidirect productDic77⋊(C3×C19)

Splittings

derived, HallC7×C11 ⋊ C3×C4×C19
HallC19×Dic77 ⋊ C3
HallC11×C19×ΓL(1,𝔽8) ⋊ C4
HallC7×C11×C19 ⋊ C3×C4
HallC19×ΓL(1,𝔽8) ⋊ Dic11
HallDic77 ⋊ C3×C19
HallC11×ΓL(1,𝔽8) ⋊ C4×C19
HallC11×C19 ⋊ ΓL(1,𝔽8)⋊C4
HallC7×C19 ⋊ C3×Dic11
HallΓL(1,𝔽8) ⋊ C19×Dic11
SylowC11 ⋊ C19×ΓL(1,𝔽8)⋊C4
SylowC7 ⋊ C3×C19×Dic11

Subgroups

subgroupG/H
center, hypercenterC2×C19C11⋊AGL(1,𝔽7)
commutator, hypocenterC7×C11C3×C4×C19
FrattiniC2C19×C11⋊AGL(1,𝔽7)
Fitting, socleC2×C7×C11×C19C2×C3
prime radicalC2×C11×C19×ΓL(1,𝔽8)C2
cosocleC2×C7×C11C2×C3×C19
LCSG ▷ C7×C11
UCSC1 ◁ C2×C19

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5852

Conjugacy classes & character table

1216 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17556, 42);