C₂×D₉₀₂₇ #49115643

order	36108
automorphism	?
homology	Abelianization (H₁) = C₂² · Schur multiplier (H₂) = C₂

Aliases

dihedral	D₁₈₀₅₄
direct product	C₂×D₉₀₂₇
unambiguous semidirect product	(C₂×C₉)⋊D₁₀₀₃
unambiguous semidirect product	(C₂×C₁₇)⋊D₅₃₁
unambiguous semidirect product	(C₂×C₅₉)⋊D₁₅₃

Splittings

Fitting	C₂×C₉×C₁₇×C₅₉ ⋊ C₂
derived, Hall	C₉×C₁₇×C₅₉ ⋊ C₂²
Hall	C₁₇×C₅₉ ⋊ C₂×D₉
Hall	C₉×C₅₉ ⋊ C₂×D₁₇
Hall	C₉×C₁₇ ⋊ C₂×D₅₉
Sylow	C₅₉ ⋊ C₂×D₁₅₃
Sylow	C₁₇ ⋊ C₂×D₅₃₁
Sylow	C₉ ⋊ C₂×D₁₀₀₃

Subgroups

	subgroup	G/H
center, hypercenter	C₂	D₉₀₂₇
commutator, cosocle, hypocenter	C₉×C₁₇×C₅₉	C₂²
Frattini	C₃	C₂×D₃₀₀₉
Fitting	C₂×C₉×C₁₇×C₅₉	C₂
socle	C₂×C₃×C₁₇×C₅₉	D₃
LCS	G ▷ C₉×C₁₇×C₅₉
UCS	C₁ ◁ C₂

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 87
transitive degree	μ_t(G) = 18054

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

Conjugacy classes & character table

9030 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36108, 22);

C2×D9027 #49115643