Finite Group Databasebeta

← Prev (#44535864) Next (#44535866) →

C4×C31×C23⋊C11 #44535865

order31372
automorphism?
homologyAbelianization (H1) = C4×C11×C31 · Schur multiplier (H2) = C1

Aliases

direct productC4×C31×C23⋊C11
unambiguous semidirect product(C4×C23)⋊(C11×C31)
unambiguous semidirect product(C4×C23×C31)⋊C11

Splittings

Fitting, HallC4×C23×C31 ⋊ C11
derived, SylowC23 ⋊ C4×C11×C31
HallC23×C31 ⋊ C4×C11
HallC4×C23 ⋊ C11×C31

Subgroups

subgroupG/H
center, hypercenterC4×C31C23⋊C11
commutator, hypocenterC23C4×C11×C31
FrattiniC2C2×C31×C23⋊C11
FittingC4×C23×C31C11
socleC2×C23×C31C2×C11
prime radicalC2×C31×C23⋊C11C2
cosocleC2×C23C2×C11×C31
LCSG ▷ C23
UCSC1 ◁ C4×C31

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2852

Conjugacy classes & character table

1612 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31372, 2);