Finite Group Databasebeta

← Prev (#32912112) Next (#32912114) →

C4×C72×C31⋊C3 #32912113

order18228
automorphism?
homologyAbelianization (H1) = C3×C4×C72 · Schur multiplier (H2) = C7

Aliases

direct productC4×C72×C31⋊C3
unambiguous semidirect product(C4×C31)⋊(C3×C72)

Splittings

Fitting, HallC4×C72×C31 ⋊ C3
derived, SylowC31 ⋊ C3×C4×C72
HallC72×C31 ⋊ C3×C4
HallC4×C31 ⋊ C3×C72

Subgroups

subgroupG/H
center, hypercenterC4×C72C31⋊C3
commutator, hypocenterC31C3×C4×C72
FrattiniC2C2×C72×C31⋊C3
FittingC4×C72×C31C3
socleC2×C72×C31C2×C3
prime radicalC2×C72×C31⋊C3C2
cosocleC2×C31C2×C3×C72
LCSG ▷ C31
UCSC1 ◁ C4×C72

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6076

Conjugacy classes & character table

2548 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18228, 121);