Finite Group Databasebeta

← Prev (#46798985) Next (#46798987) →

C7×D2415 #46798986

order33810
automorphism?
homologyAbelianization (H1) = C2×C7 · Schur multiplier (H2) = C1

Aliases

direct productC7×D2415
unambiguous semidirect productC3⋊(C7×D805)
unambiguous semidirect productC5⋊(C7×D483)
unambiguous semidirect productC7⋊(C7×D345)
unambiguous semidirect productC23⋊(C7×D105)

Splittings

Fitting, socle, HallC3×C5×C72×C23 ⋊ C2
derivedC3×C5×C7×C23 ⋊ C2×C7
HallC5×C72×C23 ⋊ D3
HallC3×C72×C23 ⋊ D5
HallC72×C23 ⋊ D15
HallC3×C5×C72 ⋊ D23
HallC3×C5×C23 ⋊ C7×D7
HallC5×C72 ⋊ D69
HallC3×C72 ⋊ D115
HallC5×C23 ⋊ C7×D21
HallC3×C23 ⋊ C7×D35
SylowC72 ⋊ D345
SylowC23 ⋊ C7×D105
HallC3×C5 ⋊ C7×D161
SylowC5 ⋊ C7×D483
SylowC3 ⋊ C7×D805

Subgroups

subgroupG/H
center, hypercenterC7D2415
commutator, cosocle, hypocenterC3×C5×C7×C23C2×C7
FrattiniC1G
Fitting, socleC3×C5×C72×C23C2
LCSG ▷ C3×C5×C7×C23
UCSC1 ◁ C7

88 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4830

Conjugacy classes & character table

8463 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33810, 90);