Finite Group Databasebeta

← Prev (#45659252) Next (#45659254) →

C17×ΓL(1,𝔽8)×Dic23 #45659253

order32844
automorphism?
homologyAbelianization (H1) = C3×C4×C17 · Schur multiplier (H2) = C1

Aliases

direct productC17×ΓL(1,𝔽8)×Dic23
unambiguous semidirect productC23⋊(C4×C17×ΓL(1,𝔽8))
unambiguous semidirect product(C7×Dic23)⋊(C3×C17)
unambiguous semidirect product(C7×C17×Dic23)⋊C3

Splittings

derived, HallC7×C23 ⋊ C3×C4×C17
HallC7×C17×Dic23 ⋊ C3
HallC17×ΓL(1,𝔽8)×C23 ⋊ C4
HallC7×C17×C23 ⋊ C3×C4
HallC7×Dic23 ⋊ C3×C17
HallΓL(1,𝔽8)×C23 ⋊ C4×C17
HallC17×C23 ⋊ C4×ΓL(1,𝔽8)
HallC7×C17 ⋊ C3×Dic23
SylowC23 ⋊ C4×C17×ΓL(1,𝔽8)
SylowC7 ⋊ C3×C17×Dic23

Subgroups

subgroupG/H
center, hypercenterC2×C17ΓL(1,𝔽8)×D23
commutator, hypocenterC7×C23C3×C4×C17
FrattiniC2C17×ΓL(1,𝔽8)×D23
Fitting, socleC2×C7×C17×C23C2×C3
prime radicalC2×C17×ΓL(1,𝔽8)×C23C2
cosocleC2×C7×C23C2×C3×C17
LCSG ▷ C7×C23
UCSC1 ◁ C2×C17

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10948

Conjugacy classes & character table

2210 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32844, 18);