Finite Group Databasebeta

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C2×C7×C17⋊(D7⋊C9) #44472563

order29988
automorphism?
homologyAbelianization (H1) = C22×C7×C9 · Schur multiplier (H2) = C2

Aliases

direct productC2×C7×C17⋊(D7⋊C9)
unambiguous semidirect product(C2×C17)⋊(C7×D7⋊C9)
unambiguous semidirect product(C2×C7⋊C9)⋊(C7×D17)
unambiguous semidirect product(C2×D119)⋊(C7×C9)

Splittings

derivedC7×C17 ⋊ C22×C7×C9
HallC7×C17×C7⋊C9 ⋊ C22
HallC2×C7×D119 ⋊ C9
HallC72×C17 ⋊ C22×C9
HallC7×C7⋊C9 ⋊ C2×D17
SylowC72 ⋊ C2×C9×D17
SylowC17 ⋊ C2×C7×D7⋊C9

Subgroups

subgroupG/H
center, hypercenterC2×C3×C7C17⋊AGL(1,𝔽7)
commutator, hypocenterC7×C17C22×C7×C9
FrattiniC3C2×C7×C17⋊AGL(1,𝔽7)
Fitting, socleC2×C3×C72×C17C2×C3
prime radicalC2×C3×C7×D119C3
cosocleC3×C7×C17C22×C3×C7
LCSG ▷ C7×C17
UCSC1 ◁ C2×C3×C7

128 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 128 conjugacy classes of subgroups — too many to draw. Only its 58 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) = 4284

Conjugacy classes & character table

1974 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29988, 204);