C₂×D₄₄₇₃ #31822027

order	17892
automorphism	?
homology	Abelianization (H₁) = C₂² · Schur multiplier (H₂) = C₂

Aliases

dihedral	D₈₉₄₆
direct product	C₂×D₄₄₇₃
unambiguous semidirect product	(C₂×C₇)⋊D₆₃₉
unambiguous semidirect product	(C₂×C₉)⋊D₄₉₇
unambiguous semidirect product	(C₂×C₇₁)⋊D₆₃

Splittings

Fitting	C₂×C₇×C₉×C₇₁ ⋊ C₂
derived, Hall	C₇×C₉×C₇₁ ⋊ C₂²
Hall	C₉×C₇₁ ⋊ C₂×D₇
Hall	C₇×C₇₁ ⋊ C₂×D₉
Sylow	C₇₁ ⋊ C₂×D₆₃
Hall	C₇×C₉ ⋊ C₂×D₇₁
Sylow	C₉ ⋊ C₂×D₄₉₇
Sylow	C₇ ⋊ C₂×D₆₃₉

Subgroups

	subgroup	G/H
center, hypercenter	C₂	D₄₄₇₃
commutator, cosocle, hypocenter	C₇×C₉×C₇₁	C₂²
Frattini	C₃	C₂×D₁₄₉₁
Fitting	C₂×C₇×C₉×C₇₁	C₂
socle	C₂×C₃×C₇×C₇₁	D₃
LCS	G ▷ C₇×C₉×C₇₁
UCS	C₁ ◁ C₂

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 89
transitive degree	μ_t(G) = 8946

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

Conjugacy classes & character table

4476 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	D₁₇₈₉₂, C₂×D₁₃₄₁₉
maximal normal subgroup of	D₁₇₈₉₂
maximal quotient of	Dic₈₉₄₆, D₁₇₈₉₂, C₂×D₁₃₄₁₉

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17892, 44);

C2×D4473 #31822027