Finite Group Databasebeta

← Prev (#46799290) Next (#46799292) →

C13×ΓL(1,𝔽8)⋊Dic31 #46799291

order33852
automorphism?
homologyAbelianization (H1) = C3×C4×C13 · Schur multiplier (H2) = C1

Aliases

direct productC13×ΓL(1,𝔽8)⋊Dic31
unambiguous semidirect productΓL(1,𝔽8)⋊(C13×Dic31)

Splittings

derived, HallC7×C31 ⋊ C3×C4×C13
HallC13×Dic217 ⋊ C3
HallC13×ΓL(1,𝔽8)×C31 ⋊ C4
HallC7×C13×C31 ⋊ C3×C4
HallDic217 ⋊ C3×C13
HallΓL(1,𝔽8)×C31 ⋊ C4×C13
HallC13×C31 ⋊ ΓL(1,𝔽8)⋊C4
HallC13×ΓL(1,𝔽8) ⋊ Dic31
HallC7×C13 ⋊ C3×Dic31
SylowC31 ⋊ C13×ΓL(1,𝔽8)⋊C4
HallΓL(1,𝔽8) ⋊ C13×Dic31
SylowC7 ⋊ C3×C13×Dic31

Subgroups

subgroupG/H
center, hypercenterC2×C13ΓL(1,𝔽8)⋊D31
commutator, hypocenterC7×C31C3×C4×C13
FrattiniC2C13×ΓL(1,𝔽8)⋊D31
Fitting, socleC2×C7×C13×C31C2×C3
prime radicalC2×C13×ΓL(1,𝔽8)×C31C2
cosocleC2×C7×C31C2×C3×C13
LCSG ▷ C7×C31
UCSC1 ◁ C2×C13

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11284

Conjugacy classes & character table

2132 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33852, 86);