C₄×C₄₉×C₆₇ #27190061

order	13132
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	?
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₁₃₁₃₂
abelian	C₄×C₄₉×C₆₇

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂×C₇	C₂×C₇×C₆₇
socle, prime radical	C₂×C₇×C₆₇	C₂×C₇
LCS	G ▷ C₁
UCS	C₁ ◁ G

18 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 120
transitive degree	μ_t(G) = 13132

A minimal faithful permutation representation — 1 generator on 120 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)(54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120)

Conjugacy classes & character table

13132 conjugacy classes. The character table is too large to display.

Relationships

derived subgroup of	Dic₁₃₁₃₂, D₂₆₂₆₄
Fitting subgroup of	D₁₃₁₃₂, Dic₆₅₆₆
maximal subgroup of	C₈×C₄₉×C₆₇, C₂×C₄×C₄₉×C₆₇, D₁₃₁₃₂, …
maximal normal subgroup of	C₈×C₄₉×C₆₇, C₂×C₄×C₄₉×C₆₇, D₁₃₁₃₂, …
maximal quotient of	C₈×C₄₉×C₆₇, C₂×C₄×C₄₉×C₆₇

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13132, 1);

C4×C49×C67 #27190061