C₂×C₃×C₇×C₁₇×C₄₃ #44502008

order	30702
nilpotency class	1
automorphism	?
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₃₀₇₀₂
abelian	C₂×C₃×C₇×C₁₇×C₄₃
multiplicative	(ℤ/30703)ˣ, (ℤ/61406)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) = 72
transitive degree	μ_t(G) = 30702

A minimal faithful permutation representation — 1 generator on 72 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)

Conjugacy classes & character table

30702 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of	Dic₁₅₃₅₁, C₂×D₁₅₃₅₁
socle of	Dic₁₅₃₅₁, C₂×D₁₅₃₅₁
maximal subgroup of	Dic₁₅₃₅₁, C₂×D₁₅₃₅₁
maximal normal subgroup of	Dic₁₅₃₅₁, C₂×D₁₅₃₅₁
automorphism group of	C₃₀₇₀₃
outer automorphism group of	C₃₀₇₀₃

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30702, 1);

C2×C3×C7×C17×C43 #44502008