Finite Group Databasebeta

← Prev (#44538325) Next (#44538327) →

C4×C43×C61⋊C3 #44538326

order31476
automorphism?
homologyAbelianization (H1) = C3×C4×C43 · Schur multiplier (H2) = C1

Aliases

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

Splittings

Fitting, HallC4×C43×C61 ⋊ C3
derived, SylowC61 ⋊ C3×C4×C43
HallC43×C61 ⋊ C3×C4
HallC4×C61 ⋊ C3×C43

Subgroups

subgroupG/H
center, hypercenterC4×C43C61⋊C3
commutator, hypocenterC61C3×C4×C43
FrattiniC2C2×C43×C61⋊C3
FittingC4×C43×C61C3
socleC2×C43×C61C2×C3
prime radicalC2×C43×C61⋊C3C2
cosocleC2×C61C2×C3×C43
LCSG ▷ C61
UCSC1 ◁ C4×C43

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10492

Conjugacy classes & character table

3956 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31476, 2);