Finite Group Databasebeta

← Prev (#44567261) Next (#44567263) →

C7×D2301 #44567262

order32214
automorphism?
homologyAbelianization (H1) = C2×C7 · Schur multiplier (H2) = C1

Aliases

direct productC7×D2301
unambiguous semidirect productC3⋊(C7×D767)
unambiguous semidirect productC13⋊(C7×D177)
unambiguous semidirect productC59⋊(C7×D39)

Splittings

Fitting, socle, HallC3×C7×C13×C59 ⋊ C2
derived, HallC3×C13×C59 ⋊ C2×C7
HallC7×C13×C59 ⋊ D3
HallC3×C7×C59 ⋊ D13
HallC13×C59 ⋊ D3×C7
HallC7×C59 ⋊ D39
HallC3×C7×C13 ⋊ D59
HallC3×C59 ⋊ C7×D13
HallC7×C13 ⋊ D177
SylowC59 ⋊ C7×D39
HallC3×C13 ⋊ C7×D59
HallC3×C7 ⋊ D767
SylowC13 ⋊ C7×D177
SylowC3 ⋊ C7×D767

Subgroups

subgroupG/H
center, hypercenterC7D2301
commutator, cosocle, hypocenterC3×C13×C59C2×C7
FrattiniC1G
Fitting, socleC3×C7×C13×C59C2
LCSG ▷ C3×C13×C59
UCSC1 ◁ C7

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 16107

Conjugacy classes & character table

8064 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32214, 16);