Finite Group Databasebeta

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C7×C5⋊(C5⋊(D7⋊C9)) #36347804

order22050
automorphism?
homologyAbelianization (H1) = C2×C7×C9 · Schur multiplier (H2) = C5

Aliases

direct productC7×C5⋊(C5⋊(D7⋊C9))
unambiguous semidirect productC5⋊(C7×C5⋊(D7⋊C9))
unambiguous semidirect product(C7⋊C9)⋊(C7×C5⋊D5)

Splittings

derivedC52×C7 ⋊ C2×C7×C9
HallC52×C7×C7⋊C9 ⋊ C2
HallC7×C5⋊D35 ⋊ C9
HallC52×C72 ⋊ C2×C9
HallC7×C7⋊C9 ⋊ C5⋊D5
SylowC72 ⋊ C9×C5⋊D5
SylowC52 ⋊ C7×D7⋊C9

Subgroups

subgroupG/H
center, hypercenterC3×C7C5⋊(C5⋊AGL(1,𝔽7))
commutator, hypocenterC52×C7C2×C7×C9
FrattiniC3C7×C5⋊(C5⋊AGL(1,𝔽7))
Fitting, socleC3×C52×C72C2×C3
prime radicalC3×C7×C5⋊D35C3
cosocleC3×C52×C7C2×C3×C7
LCSG ▷ C52×C7
UCSC1 ◁ C3×C7

208 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 86 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3150

Conjugacy classes & character table

1407 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22050, 241);