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C11×#11716322 #22578622

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

Aliases

direct productC11×#11716322

Splittings

Fitting, socle, HallC7×C11×C19 ⋊ C2×C3
derived, HallC7×C19 ⋊ C2×C3×C11
HallC11×#87705 ⋊ C2
HallC7×C11×D19 ⋊ C3
HallC11×D19 ⋊ ΓL(1,𝔽8)
Hall#87705 ⋊ C2×C11
HallC7×D19 ⋊ C3×C11
HallC11×C19 ⋊ C2×ΓL(1,𝔽8)
HallC7×C11 ⋊ D19⋊C3
HallD19 ⋊ C11×ΓL(1,𝔽8)
SylowC19 ⋊ C2×C11×ΓL(1,𝔽8)
SylowC7 ⋊ C11×D19⋊C3

Subgroups

subgroupG/H
center, hypercenterC11#11716322
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

341 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC11×#11716322⋊C2, #11716322⋊D11, D11×#11716322, …
maximal normal subgroup ofC11×#11716322⋊C2, #11716322⋊D11, D11×#11716322, …
maximal quotient ofC11×#13097583, C2×C11×#11716322, C11×#14558781, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8778, 24);