Finite Group Databasebeta

← Prev (#49085200) Next (#49085202) →

C3×C23×(C43⋊C3)⋊C4 #49085201

order35604
automorphism?
homologyAbelianization (H1) = C32×C4×C23 · Schur multiplier (H2) = C3

Aliases

direct productC3×C23×(C43⋊C3)⋊C4
unambiguous semidirect product(C43⋊C3)⋊(C3×C4×C23)
unambiguous semidirect productDic43⋊(C32×C23)
unambiguous semidirect product(C3×Dic43)⋊(C3×C23)
unambiguous semidirect product(C23×Dic43)⋊C32
unambiguous semidirect product(C3×C23×Dic43)⋊C3

Splittings

derived, SylowC43 ⋊ C32×C4×C23
HallC3×C23×C43⋊C3 ⋊ C4
HallC23×Dic43 ⋊ C32
HallC23×C43 ⋊ C32×C4
HallC3×C43⋊C3 ⋊ C4×C23
HallDic43 ⋊ C32×C23

Subgroups

subgroupG/H
center, hypercenterC2×C3×C23D43⋊C3
commutator, hypocenterC43C32×C4×C23
FrattiniC2C3×C23×D43⋊C3
Fitting, socleC2×C3×C23×C43C2×C3
prime radicalC2×C3×C23×C43⋊C3C2
cosocleC2×C43C2×C32×C23
LCSG ▷ C43
UCSC1 ◁ C2×C3×C23

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11868

Conjugacy classes & character table

1794 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35604, 36);