C₂×C₃×C₅×C₁₇×C₅₃ #41028405

order	27030
nilpotency class	1
automorphism	?
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₂₇₀₃₀
abelian	C₂×C₃×C₅×C₁₇×C₅₃
multiplicative	(ℤ/27031)ˣ, (ℤ/54062)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator, Frattini	C₁	G
LCS	G ▷ C₁
UCS	C₁ ◁ G

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 80
transitive degree	μ_t(G) = 27030

A minimal faithful permutation representation — 1 generator on 80 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)

Conjugacy classes & character table

27030 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of	Dic₁₃₅₁₅, C₂×D₁₃₅₁₅
socle of	Dic₁₃₅₁₅, C₂×D₁₃₅₁₅
maximal subgroup of	Dic₁₃₅₁₅, C₂×D₁₃₅₁₅
maximal normal subgroup of	Dic₁₃₅₁₅, C₂×D₁₃₅₁₅
automorphism group of	C₂₇₀₃₁
outer automorphism group of	C₂₇₀₃₁

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(27030, 1);

C2×C3×C5×C17×C53 #41028405