C₂×D₉₀₆₃ #49136235

order	36252
automorphism	?
homology	Abelianization (H₁) = C₂² · Schur multiplier (H₂) = C₂

Aliases

dihedral	D₁₈₁₂₆
direct product	C₂×D₉₀₆₃
unambiguous semidirect product	(C₂×C₉)⋊D₁₀₀₇
unambiguous semidirect product	(C₂×C₁₉)⋊D₄₇₇
unambiguous semidirect product	(C₂×C₅₃)⋊D₁₇₁

Splittings

Fitting	C₂×C₉×C₁₉×C₅₃ ⋊ C₂
derived, Hall	C₉×C₁₉×C₅₃ ⋊ C₂²
Hall	C₁₉×C₅₃ ⋊ C₂×D₉
Hall	C₉×C₅₃ ⋊ C₂×D₁₉
Hall	C₉×C₁₉ ⋊ C₂×D₅₃
Sylow	C₅₃ ⋊ C₂×D₁₇₁
Sylow	C₁₉ ⋊ C₂×D₄₇₇
Sylow	C₉ ⋊ C₂×D₁₀₀₇

Subgroups

	subgroup	G/H
center, hypercenter	C₂	D₉₀₆₃
commutator, cosocle, hypocenter	C₉×C₁₉×C₅₃	C₂²
Frattini	C₃	C₂×D₃₀₂₁
Fitting	C₂×C₉×C₁₉×C₅₃	C₂
socle	C₂×C₃×C₁₉×C₅₃	D₃
LCS	G ▷ C₉×C₁₉×C₅₃
UCS	C₁ ◁ C₂

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 83
transitive degree	μ_t(G) = 18126

A minimal faithful permutation representation — 2 generators on 83 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);(4,11)(5,10)(6,9)(7,8)(13,30)(14,29)(15,28)(16,27)(17,26)(18,25)(19,24)(20,23)(21,22)(32,83)(33,82)(34,81)(35,80)(36,79)(37,78)(38,77)(39,76)(40,75)(41,74)(42,73)(43,72)(44,71)(45,70)(46,69)(47,68)(48,67)(49,66)(50,65)(51,64)(52,63)(53,62)(54,61)(55,60)(56,59)(57,58)

Conjugacy classes & character table

9066 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36252, 34);

C2×D9063 #49136235