Finite Group Databasebeta

← Prev (#30628135) Next (#30628137) →

C7×C3⋊(C11⋊#595) #30628136

order15708
automorphism?
homologyAbelianization (H1) = C4×C7 · Schur multiplier (H2) = C1

Aliases

direct productC7×C3⋊(C11⋊#595)
unambiguous semidirect productC3⋊(C7×C11⋊#595)
unambiguous semidirect productC11⋊(C7×C3⋊#595)

Splittings

Fitting, socle, HallC3×C7×C11×C17 ⋊ C4
derived, HallC3×C11×C17 ⋊ C4×C7
HallC7×C11×C17 ⋊ Dic3
HallC3×C7×C17 ⋊ Dic11
HallC3×C7×C11 ⋊ #595
HallC11×C17 ⋊ C7×Dic3
HallC7×C17 ⋊ Dic33
HallC7×C11 ⋊ C3⋊#595
HallC3×C17 ⋊ C7×Dic11
HallC3×C11 ⋊ C7×#595
HallC3×C7 ⋊ C11⋊#595
SylowC17 ⋊ C7×Dic33
SylowC11 ⋊ C7×C3⋊#595
SylowC3 ⋊ C7×C11⋊#595

Subgroups

subgroupG/H
center, hypercenterC7C3⋊(C11⋊#595)
commutator, hypocenterC3×C11×C17C4×C7
FrattiniC1G
Fitting, socleC3×C7×C11×C17C4
prime radicalC3×C7×C11×D17C2
cosocleC3×C11×D17C2×C7
LCSG ▷ C3×C11×C17
UCSC1 ◁ C7

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3927

Conjugacy classes & character table

1176 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15708, 57);