Finite Group Databasebeta

← Prev (#30628141) Next (#30628143) →

C11×C3⋊(C7⋊#595) #30628142

order15708
automorphism?
homologyAbelianization (H1) = C4×C11 · Schur multiplier (H2) = C1

Aliases

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

Splittings

Fitting, socle, HallC3×C7×C11×C17 ⋊ C4
derived, HallC3×C7×C17 ⋊ C4×C11
HallC7×C11×C17 ⋊ Dic3
HallC3×C11×C17 ⋊ Dic7
HallC3×C7×C11 ⋊ #595
HallC11×C17 ⋊ Dic21
HallC7×C17 ⋊ C11×Dic3
HallC7×C11 ⋊ C3⋊#595
HallC3×C17 ⋊ C11×Dic7
HallC3×C11 ⋊ C7⋊#595
HallC3×C7 ⋊ C11×#595
SylowC17 ⋊ C11×Dic21
SylowC7 ⋊ C11×C3⋊#595
SylowC3 ⋊ C11×C7⋊#595

Subgroups

subgroupG/H
center, hypercenterC11C3⋊(C7⋊#595)
commutator, hypocenterC3×C7×C17C4×C11
FrattiniC1G
Fitting, socleC3×C7×C11×C17C4
prime radicalC3×C7×C11×D17C2
cosocleC3×C7×D17C2×C11
LCSG ▷ C3×C7×C17
UCSC1 ◁ C11

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3927

Conjugacy classes & character table

1188 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15708, 63);