Finite Group Databasebeta

← Prev (#37558815) Next (#37558817) →

C5×C11×D217 #37558816

order23870
automorphism?
homologyAbelianization (H1) = C2×C5×C11 · Schur multiplier (H2) = C1

Aliases

direct productC5×C11×D217
unambiguous semidirect productC7⋊(C5×C11×D31)

Splittings

Fitting, socle, HallC5×C7×C11×C31 ⋊ C2
derived, HallC7×C31 ⋊ C2×C5×C11
HallC7×C11×C31 ⋊ C2×C5
HallC5×C11×C31 ⋊ D7
HallC5×C7×C31 ⋊ C2×C11
HallC5×C7×C11 ⋊ D31
HallC11×C31 ⋊ C5×D7
HallC5×C31 ⋊ C11×D7
HallC7×C11 ⋊ C5×D31
HallC5×C7 ⋊ C11×D31
SylowC31 ⋊ C5×C11×D7
SylowC7 ⋊ C5×C11×D31

Subgroups

subgroupG/H
center, hypercenterC5×C11D217
commutator, cosocle, hypocenterC7×C31C2×C5×C11
FrattiniC1G
Fitting, socleC5×C7×C11×C31C2
LCSG ▷ C7×C31
UCSC1 ◁ C5×C11

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11935

Conjugacy classes & character table

6050 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23870, 12);