Finite Group Databasebeta

← Prev (#44446542) Next (#44446544) →

C4×C37×C67⋊C3 #44446543

order29748
automorphism?
homologyAbelianization (H1) = C3×C4×C37 · Schur multiplier (H2) = C1

Aliases

direct productC4×C37×C67⋊C3
unambiguous semidirect product(C4×C67)⋊(C3×C37)

Splittings

Fitting, HallC4×C37×C67 ⋊ C3
derived, SylowC67 ⋊ C3×C4×C37
HallC37×C67 ⋊ C3×C4
HallC4×C67 ⋊ C3×C37

Subgroups

subgroupG/H
center, hypercenterC4×C37C67⋊C3
commutator, hypocenterC67C3×C4×C37
FrattiniC2C2×C37×C67⋊C3
FittingC4×C37×C67C3
socleC2×C37×C67C2×C3
prime radicalC2×C37×C67⋊C3C2
cosocleC2×C67C2×C3×C37
LCSG ▷ C67
UCSC1 ◁ C4×C37

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9916

Conjugacy classes & character table

3700 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29748, 2);