Finite Group Databasebeta

← Prev (#28357490) Next (#28357492) →

C11⋊C5×C3⋊Dic21 #28357491

order13860
automorphism?
homologyAbelianization (H1) = C4×C5 · Schur multiplier (H2) = C3

Aliases

direct productC11⋊C5×C3⋊Dic21
unambiguous semidirect productC3⋊(C11⋊C5×Dic21)
unambiguous semidirect productC7⋊(C3⋊Dic3×C11⋊C5)
unambiguous semidirect product(C11×C3⋊Dic21)⋊C5

Splittings

derived, HallC32×C7×C11 ⋊ C4×C5
HallC32×C7×C11⋊C5 ⋊ C4
HallC11×C3⋊Dic21 ⋊ C5
HallC32×C11⋊C5 ⋊ Dic7
HallC7×C11⋊C5 ⋊ C3⋊Dic3
HallC32×C11 ⋊ C5×Dic7
HallC7×C11 ⋊ C5×C3⋊Dic3
HallC32×C7 ⋊ C4×C11⋊C5
SylowC11 ⋊ C5×C3⋊Dic21
SylowC32 ⋊ Dic7×C11⋊C5
SylowC7 ⋊ C3⋊Dic3×C11⋊C5

Subgroups

subgroupG/H
center, Frattini, hypercenterC2C11⋊C5×C3⋊D21
commutator, hypocenterC32×C7×C11C4×C5
Fitting, socle, cosocleC2×C32×C7×C11C2×C5
prime radicalC2×C32×C7×C11⋊C5C2
LCSG ▷ C32×C7×C11
UCSC1 ◁ C2

144 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2772

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13860, 158);