Finite Group Databasebeta

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C3×C7⋊(C11⋊#595) #30628128

order15708
automorphism?
homologyAbelianization (H1) = C3×C4 · Schur multiplier (H2) = C1

Aliases

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

Splittings

Fitting, socle, HallC3×C7×C11×C17 ⋊ C4
derived, HallC7×C11×C17 ⋊ C3×C4
HallC3×C11×C17 ⋊ Dic7
HallC3×C7×C17 ⋊ Dic11
HallC3×C7×C11 ⋊ #595
HallC11×C17 ⋊ C3×Dic7
HallC7×C17 ⋊ C3×Dic11
HallC7×C11 ⋊ C3×#595
HallC3×C17 ⋊ Dic77
HallC3×C11 ⋊ C7⋊#595
HallC3×C7 ⋊ C11⋊#595
SylowC17 ⋊ C3×Dic77
SylowC11 ⋊ C3×C7⋊#595
SylowC7 ⋊ C3×C11⋊#595

Subgroups

subgroupG/H
center, hypercenterC3C7⋊(C11⋊#595)
commutator, hypocenterC7×C11×C17C3×C4
FrattiniC1G
Fitting, socleC3×C7×C11×C17C4
prime radicalC3×C7×C11×D17C2
cosocleC7×C11×D17C2×C3
LCSG ▷ C7×C11×C17
UCSC1 ◁ C3

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3927

Conjugacy classes & character table

1164 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15708, 49);