Finite Group Databasebeta

← Prev (#32915446) Next (#32915448) →

C17×ΓL(1,𝔽8)⋊Dic13 #32915447

order18564
automorphism?
homologyAbelianization (H1) = C3×C4×C17 · Schur multiplier (H2) = C1

Aliases

direct productC17×ΓL(1,𝔽8)⋊Dic13
unambiguous semidirect productΓL(1,𝔽8)⋊(C17×Dic13)

Splittings

derived, HallC7×C13 ⋊ C3×C4×C17
HallC17×Dic91 ⋊ C3
HallC13×C17×ΓL(1,𝔽8) ⋊ C4
HallC7×C13×C17 ⋊ C3×C4
HallDic91 ⋊ C3×C17
HallC17×ΓL(1,𝔽8) ⋊ Dic13
HallC13×ΓL(1,𝔽8) ⋊ C4×C17
HallC13×C17 ⋊ ΓL(1,𝔽8)⋊C4
HallC7×C17 ⋊ C3×Dic13
HallΓL(1,𝔽8) ⋊ C17×Dic13
SylowC13 ⋊ C17×ΓL(1,𝔽8)⋊C4
SylowC7 ⋊ C3×C17×Dic13

Subgroups

subgroupG/H
center, hypercenterC2×C17ΓL(1,𝔽8)⋊D13
commutator, hypocenterC7×C13C3×C4×C17
FrattiniC2C17×ΓL(1,𝔽8)⋊D13
Fitting, socleC2×C7×C13×C17C2×C3
prime radicalC2×C13×C17×ΓL(1,𝔽8)C2
cosocleC2×C7×C13C2×C3×C17
LCSG ▷ C7×C13
UCSC1 ◁ C2×C17

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6188

Conjugacy classes & character table

1258 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18564, 42);