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C11⋊#11716321 #22578629

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

Aliases

unambiguous semidirect productC11⋊#11716321

Splittings

Fitting, socle, derived, HallC7×C11×C19 ⋊ C2×C3
HallC11×#87704 ⋊ C2
HallC7×D209 ⋊ C3
HallD209 ⋊ ΓL(1,𝔽8)
Hall#87704 ⋊ D11
HallC11×C19 ⋊ C2×ΓL(1,𝔽8)
HallC7×C19 ⋊ C3×D11
HallC7×C11 ⋊ D19⋊C3
SylowC19 ⋊ ΓL(1,𝔽8)×D11
SylowC11 ⋊ #11716321
SylowC7 ⋊ C11⋊(D19⋊C3)

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC7×C11×C19C2×C3
LCSG ▷ C7×C11×C19
UCSC1

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Polycyclic presentation:

2,3,7,11,19|d^a=d^10,e^a=e^18,c^b=c^2,e^b=e^7

Conjugacy classes & character table

266 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#11716325⋊D11, #11716327⋊D11, D11×#11716321, …
maximal normal subgroup of#11716325⋊D11, #11716327⋊D11, D11×#11716321, …
maximal quotient ofC11⋊#13097582, C2×C11⋊#11716321, C11⋊#14558780, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8778, 31);