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C17×ΓL(1,𝔽8)⋊Dic19 #41029481

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

Aliases

direct productC17×ΓL(1,𝔽8)⋊Dic19
unambiguous semidirect productΓL(1,𝔽8)⋊(C17×Dic19)

Splittings

derived, HallC7×C19 ⋊ C3×C4×C17
HallC17×Dic133 ⋊ C3
HallC17×C19×ΓL(1,𝔽8) ⋊ C4
HallC7×C17×C19 ⋊ C3×C4
HallDic133 ⋊ C3×C17
HallC19×ΓL(1,𝔽8) ⋊ C4×C17
HallC17×ΓL(1,𝔽8) ⋊ Dic19
HallC17×C19 ⋊ ΓL(1,𝔽8)⋊C4
HallC7×C17 ⋊ C3×Dic19
HallΓL(1,𝔽8) ⋊ C17×Dic19
SylowC19 ⋊ C17×ΓL(1,𝔽8)⋊C4
SylowC7 ⋊ C3×C17×Dic19

Subgroups

subgroupG/H
center, hypercenterC2×C17ΓL(1,𝔽8)⋊D19
commutator, hypocenterC7×C19C3×C4×C17
FrattiniC2C17×ΓL(1,𝔽8)⋊D19
Fitting, socleC2×C7×C17×C19C2×C3
prime radicalC2×C17×C19×ΓL(1,𝔽8)C2
cosocleC2×C7×C19C2×C3×C17
LCSG ▷ C7×C19
UCSC1 ◁ C2×C17

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9044

Conjugacy classes & character table

1768 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(27132, 38);