C₂²×C₇×C₉×C₆₁ #29506715

order	15372
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	?
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂

Aliases

abelian	C₂²×C₇×C₉×C₆₁
multiplicative	(ℤ/23061)ˣ, (ℤ/30748)ˣ, (ℤ/46122)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₃	C₂²×C₃×C₇×C₆₁
socle, prime radical	C₂²×C₃×C₇×C₆₁	C₃
LCS	G ▷ C₁
UCS	C₁ ◁ G

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 81
transitive degree	μ_t(G) = 15372

A minimal faithful permutation representation — 2 generators on 81 points:

(1,2)(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);(3,4)

Conjugacy classes & character table

15372 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×C₄×C₇×C₉×C₆₁, C₂³×C₇×C₉×C₆₁
maximal normal subgroup of	C₂×C₄×C₇×C₉×C₆₁, C₂³×C₇×C₉×C₆₁
maximal quotient of	C₂×C₄×C₇×C₉×C₆₁, C₂³×C₇×C₉×C₆₁

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15372, 25);

C22×C7×C9×C61 #29506715