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C11×#11716325 #22578633

order8778
automorphism?
homologyAbelianization (H1) = C2×C3×C11 · Schur multiplier (H2) = C1

Aliases

direct productC11×#11716325

Splittings

Fitting, socle, HallC7×C11×C19 ⋊ C2×C3
derived, HallC7×C19 ⋊ C2×C3×C11
HallC11×#87704 ⋊ C2
HallC11×D7×C19 ⋊ C3
Hall#87704 ⋊ C2×C11
HallD7×C19 ⋊ C3×C11
HallC11×C19 ⋊ AGL(1,𝔽7)
HallC11×D7 ⋊ C19⋊C3
HallC7×C11 ⋊ C2×C19⋊C3
SylowC19 ⋊ C11×AGL(1,𝔽7)
HallD7 ⋊ C11×C19⋊C3
SylowC7 ⋊ C2×C11×C19⋊C3

Subgroups

subgroupG/H
center, hypercenterC11#11716325
commutator, hypocenterC7×C19C2×C3×C11
FrattiniC1G
Fitting, socleC7×C11×C19C2×C3
LCSG ▷ C7×C19
UCSC1 ◁ C11

32 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

407 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC11×#11716321⋊C2, #11716325⋊D11, D11×#11716325, …
maximal normal subgroup ofC11×#11716321⋊C2, #11716325⋊D11, D11×#11716325, …
maximal quotient ofC11×#13097586, C2×C11×#11716325, C11×#14558784, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8778, 35);