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D5×C13×C7⋊C9 #22551200

order8190
automorphism?
homologyAbelianization (H1) = C2×C9×C13 · Schur multiplier (H2) = C1

Aliases

direct productD5×C13×C7⋊C9
unambiguous semidirect productC5⋊(C2×C13×C7⋊C9)
unambiguous semidirect product(C7×D5)⋊(C9×C13)

Splittings

derived, HallC5×C7 ⋊ C2×C9×C13
HallC5×C13×C7⋊C9 ⋊ C2
HallC7×D5×C13 ⋊ C9
HallC5×C7×C13 ⋊ C2×C9
HallC5×C7⋊C9 ⋊ C2×C13
HallC7×C13 ⋊ C9×D5
HallC7×D5 ⋊ C9×C13
HallC5×C13 ⋊ C2×C7⋊C9
SylowC7 ⋊ C9×D5×C13
SylowC5 ⋊ C2×C13×C7⋊C9

Subgroups

subgroupG/H
center, hypercenterC3×C13D5×ΓL(1,𝔽8)
commutator, hypocenterC5×C7C2×C9×C13
FrattiniC3D5×C13×ΓL(1,𝔽8)
Fitting, socleC3×C5×C7×C13C2×C3
LCSG ▷ C5×C7
UCSC1 ◁ C3×C13

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

780 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC13×(C7⋊C9)⋊AGL(1,𝔽5), (C7⋊C9)⋊#63120, C13×AGL(1,𝔽5)×C7⋊C9, …
maximal normal subgroup ofC13×(C7⋊C9)⋊AGL(1,𝔽5), (C7⋊C9)⋊#63120, C13×AGL(1,𝔽5)×C7⋊C9, …
maximal quotient ofC13×Dic5×C7⋊C9, C2×D5×C13×C7⋊C9

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8190, 34);