C₁₁×D₅₇ #11929423

order	1254
isoclinism	isoclinic class of D₅₇
automorphism	?
homology	Abelianization (H₁) = C₂×C₁₁ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₁₁×D₅₇
unambiguous semidirect product	C₃⋊(C₁₁×D₁₉)
unambiguous semidirect product	C₁₉⋊(D₃×C₁₁)

Splittings

Fitting, socle, Hall	C₃×C₁₁×C₁₉ ⋊ C₂
derived, Hall	C₃×C₁₉ ⋊ C₂×C₁₁
Hall	C₁₁×C₁₉ ⋊ D₃
Hall	C₃×C₁₁ ⋊ D₁₉
Sylow	C₁₉ ⋊ D₃×C₁₁
Sylow	C₃ ⋊ C₁₁×D₁₉

Subgroups

	subgroup	G/H
center, hypercenter	C₁₁	D₅₇
commutator, cosocle, hypocenter	C₃×C₁₉	C₂×C₁₁
Frattini	C₁	G
Fitting, socle	C₃×C₁₁×C₁₉	C₂
LCS	G ▷ C₃×C₁₉
UCS	C₁ ◁ C₁₁

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 33
transitive degree	μ_t(G) = 627

A minimal faithful permutation representation — 2 generators on 33 points:

(1,2,3,4,5,6,7,8,9,10,11)(12,13,14)(15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33);(13,14)(16,33)(17,32)(18,31)(19,30)(20,29)(21,28)(22,27)(23,26)(24,25)

Conjugacy classes & character table

330 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	D₃×C₁₁×D₁₉, D₁₁×D₅₇, D₃₃⋊D₁₉, …
maximal normal subgroup of	D₃×C₁₁×D₁₉, D₁₁×D₅₇, D₃₃⋊D₁₉, …
maximal quotient of	C₁₁×Dic₅₇, C₂×C₁₁×D₅₇, C₁₁×D₁₇₁, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1254, 9);

C11×D57 #11929423