Finite Group Databasebeta

← Prev (#44445707) Next (#44445709) →

C4×ΓL(1,𝔽8)×C353 #44445708

order29652
automorphism?
homologyAbelianization (H1) = C3×C4×C353 · Schur multiplier (H2) = C1

Aliases

direct productC4×ΓL(1,𝔽8)×C353
unambiguous semidirect product(C4×C7)⋊(C3×C353)
unambiguous semidirect product(C4×C7×C353)⋊C3

Splittings

Fitting, HallC4×C7×C353 ⋊ C3
derived, SylowC7 ⋊ C3×C4×C353
HallC7×C353 ⋊ C3×C4
HallC4×C7 ⋊ C3×C353

Subgroups

subgroupG/H
center, hypercenterC4×C353ΓL(1,𝔽8)
commutator, hypocenterC7C3×C4×C353
FrattiniC2C2×ΓL(1,𝔽8)×C353
FittingC4×C7×C353C3
socleC2×C7×C353C2×C3
prime radicalC2×ΓL(1,𝔽8)×C353C2
cosocleC2×C7C2×C3×C353
LCSG ▷ C7
UCSC1 ◁ C4×C353

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9884

Conjugacy classes & character table

7060 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29652, 2);