C₁₃×D₁₁×D₂₃ #27190451

order	13156
automorphism	?
homology	Abelianization (H₁) = C₂²×C₁₃ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₁₃×D₁₁×D₂₃
unambiguous semidirect product	(D₁₁×C₂₃)⋊(C₂×C₁₃)
unambiguous semidirect product	(C₁₁×D₂₃)⋊(C₂×C₁₃)
unambiguous semidirect product	D₂₅₃⋊(C₂×C₁₃)

Splittings

Fitting, socle, Hall	C₁₁×C₁₃×C₂₃ ⋊ C₂²
derived, Hall	C₁₁×C₂₃ ⋊ C₂²×C₁₃
Hall	C₁₃×C₂₃ ⋊ C₂×D₁₁
Hall	C₁₁×C₁₃ ⋊ C₂×D₂₃
Sylow	C₂₃ ⋊ C₂×C₁₃×D₁₁
Sylow	C₁₁ ⋊ C₂×C₁₃×D₂₃

Subgroups

	subgroup	G/H
center, hypercenter	C₁₃	D₁₁×D₂₃
commutator, cosocle, hypocenter	C₁₁×C₂₃	C₂²×C₁₃
Frattini	C₁	G
Fitting, socle	C₁₁×C₁₃×C₂₃	C₂²
LCS	G ▷ C₁₁×C₂₃
UCS	C₁ ◁ C₁₃

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 47
transitive degree	μ_t(G) = 3289

A minimal faithful permutation representation — 2 generators on 47 points:

(2,3)(4,5)(6,7)(8,9)(10,11)(12,13)(14,15)(16,17)(18,19)(20,21)(22,23)(24,25,27,29,31,33,34,32,30,28,26)(35,36,37,38,39,40,41,42,43,44,45,46,47);(1,2,4,6,8,10,12,14,16,18,20,22,23,21,19,17,15,13,11,9,7,5,3)(25,26)(27,28)(29,30)(31,32)(33,34)

Conjugacy classes & character table

1183 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13156, 24);

C13×D11×D23 #27190451