C₄×C₉×C₁₃×C₂₉ #28330843

order	13572
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	?
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₁₃₅₇₂
abelian	C₄×C₉×C₁₃×C₂₉

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂×C₃	C₂×C₃×C₁₃×C₂₉
socle, prime radical	C₂×C₃×C₁₃×C₂₉	C₂×C₃
LCS	G ▷ C₁
UCS	C₁ ◁ G

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 55
transitive degree	μ_t(G) = 13572

A minimal faithful permutation representation — 1 generator on 55 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)

Conjugacy classes & character table

13572 conjugacy classes. The character table is too large to display.

Relationships

derived subgroup of	Dic₁₃₅₇₂, D₂₇₁₄₄
Fitting subgroup of	D₁₃₅₇₂, Dic₆₇₈₆
maximal subgroup of	C₈×C₉×C₁₃×C₂₉, C₂×C₄×C₉×C₁₃×C₂₉, D₁₃₅₇₂, …
maximal normal subgroup of	C₈×C₉×C₁₃×C₂₉, C₂×C₄×C₉×C₁₃×C₂₉, D₁₃₅₇₂, …
maximal quotient of	C₈×C₉×C₁₃×C₂₉, C₂×C₄×C₉×C₁₃×C₂₉

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13572, 1);

C4×C9×C13×C29 #28330843