Finite Group Databasebeta

← Prev (#37558819) Next (#37558821) →

C7×C11×D155 #37558820

order23870
automorphism?
homologyAbelianization (H1) = C2×C7×C11 · Schur multiplier (H2) = C1

Aliases

direct productC7×C11×D155
unambiguous semidirect productC5⋊(C7×C11×D31)
unambiguous semidirect productC31⋊(C7×D5×C11)

Splittings

Fitting, socle, HallC5×C7×C11×C31 ⋊ C2
derived, HallC5×C31 ⋊ C2×C7×C11
HallC7×C11×C31 ⋊ D5
HallC5×C11×C31 ⋊ C2×C7
HallC5×C7×C31 ⋊ C2×C11
HallC5×C7×C11 ⋊ D31
HallC11×C31 ⋊ C7×D5
HallC7×C31 ⋊ D5×C11
HallC5×C11 ⋊ C7×D31
HallC5×C7 ⋊ C11×D31
SylowC31 ⋊ C7×D5×C11
SylowC5 ⋊ C7×C11×D31

Subgroups

subgroupG/H
center, hypercenterC7×C11D155
commutator, cosocle, hypocenterC5×C31C2×C7×C11
FrattiniC1G
Fitting, socleC5×C7×C11×C31C2
LCSG ▷ C5×C31
UCSC1 ◁ C7×C11

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11935

Conjugacy classes & character table

6083 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23870, 16);