Finite Group Databasebeta

← Prev (#46799208) Next (#46799210) →

C4×C7×#11925882 #46799209

order33852
automorphism?
homologyAbelianization (H1) = C3×C4×C7 · Schur multiplier (H2) = C1

Aliases

direct productC4×C7×#11925882

Splittings

Fitting, HallC4×C7×C13×C31 ⋊ C3
derived, HallC13×C31 ⋊ C3×C4×C7
HallC7×C13×C31 ⋊ C3×C4
HallC4×C13×C31 ⋊ C3×C7
HallC4×C7×C31 ⋊ C13⋊C3
HallC4×C7×C13 ⋊ C31⋊C3
HallC7×C31 ⋊ C4×C13⋊C3
HallC4×C31 ⋊ C7×C13⋊C3
HallC7×C13 ⋊ C4×C31⋊C3
HallC4×C13 ⋊ C7×C31⋊C3
SylowC31 ⋊ C4×C7×C13⋊C3
SylowC13 ⋊ C4×C7×C31⋊C3

Subgroups

subgroupG/H
center, hypercenterC4×C7#11925882
commutator, hypocenterC13×C31C3×C4×C7
FrattiniC2C2×C7×#11925882
FittingC4×C7×C13×C31C3
socleC2×C7×C13×C31C2×C3
prime radicalC2×C7×#11925882C2
cosocleC2×C13×C31C2×C3×C7
LCSG ▷ C13×C31
UCSC1 ◁ C4×C7

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11284

Conjugacy classes & character table

3836 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33852, 4);