Finite Group Databasebeta

← Prev (#44538326) Next (#44538328) →

C4×C61×C43⋊C3 #44538327

order31476
automorphism?
homologyAbelianization (H1) = C3×C4×C61 · Schur multiplier (H2) = C1

Aliases

direct productC4×C61×C43⋊C3
unambiguous semidirect product(C4×C43)⋊(C3×C61)

Splittings

Fitting, HallC4×C43×C61 ⋊ C3
derived, SylowC43 ⋊ C3×C4×C61
HallC43×C61 ⋊ C3×C4
HallC4×C43 ⋊ C3×C61

Subgroups

subgroupG/H
center, hypercenterC4×C61C43⋊C3
commutator, hypocenterC43C3×C4×C61
FrattiniC2C2×C61×C43⋊C3
FittingC4×C43×C61C3
socleC2×C43×C61C2×C3
prime radicalC2×C61×C43⋊C3C2
cosocleC2×C43C2×C3×C61
LCSG ▷ C43
UCSC1 ◁ C4×C61

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10492

Conjugacy classes & character table

4148 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31476, 3);