C₂×D₄₆₅₅ #32916004

order	18620
automorphism	?
homology	Abelianization (H₁) = C₂² · Schur multiplier (H₂) = C₂

Aliases

dihedral	D₉₃₁₀
direct product	C₂×D₄₆₅₅
unambiguous semidirect product	(C₂×C₅)⋊D₉₃₁
unambiguous semidirect product	(C₂×C₁₉)⋊D₂₄₅
unambiguous semidirect product	(C₂×C₄₉)⋊D₉₅

Splittings

Fitting	C₂×C₅×C₁₉×C₄₉ ⋊ C₂
derived, Hall	C₅×C₁₉×C₄₉ ⋊ C₂²
Hall	C₁₉×C₄₉ ⋊ C₂×D₅
Hall	C₅×C₄₉ ⋊ C₂×D₁₉
Hall	C₅×C₁₉ ⋊ C₂×D₄₉
Sylow	C₄₉ ⋊ C₂×D₉₅
Sylow	C₁₉ ⋊ C₂×D₂₄₅
Sylow	C₅ ⋊ C₂×D₉₃₁

Subgroups

	subgroup	G/H
center, hypercenter	C₂	D₄₆₅₅
commutator, cosocle, hypocenter	C₅×C₁₉×C₄₉	C₂²
Frattini	C₇	C₂×D₆₆₅
Fitting	C₂×C₅×C₁₉×C₄₉	C₂
socle	C₂×C₅×C₇×C₁₉	D₇
LCS	G ▷ C₅×C₁₉×C₄₉
UCS	C₁ ◁ C₂

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 75
transitive degree	μ_t(G) = 9310

A minimal faithful permutation representation — 2 generators on 75 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);(4,7)(5,6)(9,56)(10,55)(11,54)(12,53)(13,52)(14,51)(15,50)(16,49)(17,48)(18,47)(19,46)(20,45)(21,44)(22,43)(23,42)(24,41)(25,40)(26,39)(27,38)(28,37)(29,36)(30,35)(31,34)(32,33)(58,75)(59,74)(60,73)(61,72)(62,71)(63,70)(64,69)(65,68)(66,67)

Conjugacy classes & character table

4658 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	D₁₈₆₂₀, C₂×D₁₃₉₆₅
maximal normal subgroup of	D₁₈₆₂₀
maximal quotient of	Dic₉₃₁₀, D₁₈₆₂₀, C₂×D₁₃₉₆₅

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18620, 21);

C2×D4655 #32916004