D₁₅₄₃₃ #44525222

order	30866
automorphism	?
homology	Abelianization (H₁) = C₂ · Schur multiplier (H₂) = C₁

Aliases

dihedral	D₁₅₄₃₃
unambiguous semidirect product	C₁₁⋊D₁₄₀₃
unambiguous semidirect product	C₂₃⋊D₆₇₁
unambiguous semidirect product	C₆₁⋊D₂₅₃

Splittings

Fitting, socle, derived, Hall	C₁₁×C₂₃×C₆₁ ⋊ C₂
Hall	C₂₃×C₆₁ ⋊ D₁₁
Hall	C₁₁×C₆₁ ⋊ D₂₃
Hall	C₁₁×C₂₃ ⋊ D₆₁
Sylow	C₆₁ ⋊ D₂₅₃
Sylow	C₂₃ ⋊ D₆₇₁
Sylow	C₁₁ ⋊ D₁₄₀₃

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₁₁×C₂₃×C₆₁	C₂
LCS	G ▷ C₁₁×C₂₃×C₆₁
UCS	C₁

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 95
transitive degree	μ_t(G) = 15433

A minimal faithful permutation representation — 2 generators on 95 points:

(1,2,3,4,5,6,7,8,9,10,11)(12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34)(35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95);(2,11)(3,10)(4,9)(5,8)(6,7)(13,34)(14,33)(15,32)(16,31)(17,30)(18,29)(19,28)(20,27)(21,26)(22,25)(23,24)(36,95)(37,94)(38,93)(39,92)(40,91)(41,90)(42,89)(43,88)(44,87)(45,86)(46,85)(47,84)(48,83)(49,82)(50,81)(51,80)(52,79)(53,78)(54,77)(55,76)(56,75)(57,74)(58,73)(59,72)(60,71)(61,70)(62,69)(63,68)(64,67)(65,66)

Polycyclic presentation:

2,11,23,61|b^a=b^10,c^a=c^22,d^a=d^60

Conjugacy classes & character table

7718 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×D₁₅₄₃₃
maximal normal subgroup of	C₂×D₁₅₄₃₃
maximal quotient of	Dic₁₅₄₃₃, C₂×D₁₅₄₃₃

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30866, 9);

D15433 #44525222