Finite Group Databasebeta

← Prev (#20301330) Next (#20301332) →

C7×C3⋊(C5⋊D35) #20301331

order7350
automorphism?
homologyAbelianization (H1) = C2×C7 · Schur multiplier (H2) = C5

Aliases

direct productC7×C3⋊(C5⋊D35)
unambiguous semidirect productC3⋊(C7×C5⋊D35)
unambiguous semidirect productC5⋊(C7×D105)
unambiguous semidirect productC7⋊(C7×C3⋊(C5⋊D5))

Splittings

Fitting, socle, HallC3×C52×C72 ⋊ C2
derivedC3×C52×C7 ⋊ C2×C7
HallC52×C72 ⋊ D3
HallC3×C72 ⋊ C5⋊D5
HallC3×C52 ⋊ C7×D7
SylowC72 ⋊ C3⋊(C5⋊D5)
SylowC52 ⋊ C7×D21
SylowC3 ⋊ C7×C5⋊D35

Subgroups

subgroupG/H
center, hypercenterC7C3⋊(C5⋊D35)
commutator, hypocenterC3×C52×C7C2×C7
FrattiniC1G
Fitting, socleC3×C52×C72C2
LCSG ▷ C3×C52×C7
UCSC1 ◁ C7

176 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1848 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC7×D7×C3⋊(C5⋊D5), D7×C3⋊(C5⋊D35), #28413530, …
maximal normal subgroup ofC7×D7×C3⋊(C5⋊D5), D7×C3⋊(C5⋊D35), #28413530, …
maximal quotient ofC7×C3⋊(C7⋊#1039), C2×C7×C3⋊(C5⋊D35), C7×C5⋊D315, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7350, 154);