Finite Group Databasebeta

← Prev (#26039464) Next (#26039466) →

C13×(C7⋊C9)⋊D7 #26039465

order11466
automorphism?
homologyAbelianization (H1) = C2×C9×C13 · Schur multiplier (H2) = C1

Aliases

direct productC13×(C7⋊C9)⋊D7
unambiguous semidirect product(C7⋊C9)⋊(C13×D7)

Splittings

derived, SylowC72 ⋊ C2×C9×C13
HallC7×C13×C7⋊C9 ⋊ C2
HallC13×C7⋊D7 ⋊ C9
HallC72×C13 ⋊ C2×C9
HallC7×C7⋊C9 ⋊ C2×C13
HallC7⋊D7 ⋊ C9×C13

Subgroups

subgroupG/H
center, hypercenterC3×C13ΓL(1,𝔽8)⋊D7
commutator, hypocenterC72C2×C9×C13
FrattiniC3C13×ΓL(1,𝔽8)⋊D7
Fitting, socleC3×C72×C13C2×C3
prime radicalC3×C13×C7⋊D7C3
cosocleC3×C72C2×C3×C13
LCSG ▷ C72
UCSC1 ◁ C3×C13

64 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

858 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC13×D7×D7⋊C9, ((C7⋊C9)⋊D7)⋊D13, D13×(C7⋊C9)⋊D7, …
maximal normal subgroup ofC13×D7×D7⋊C9, ((C7⋊C9)⋊D7)⋊D13, D13×(C7⋊C9)⋊D7, …
maximal quotient ofC13×(C7⋊C9)⋊Dic7, C2×C13×(C7⋊C9)⋊D7

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11466, 108);