C₂²×C₁₁×C₂₃×C₂₅ #38760680

order	25300
nilpotency class	1
automorphism	?
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂

Aliases

abelian	C₂²×C₁₁×C₂₃×C₂₅
multiplicative	(ℤ/26473)ˣ, (ℤ/52946)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₅	C₂²×C₅×C₁₁×C₂₃
socle, prime radical	C₂²×C₅×C₁₁×C₂₃	C₅
LCS	G ▷ C₁
UCS	C₁ ◁ G

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 63
transitive degree	μ_t(G) = 25300

A minimal faithful permutation representation — 2 generators on 63 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);(3,4)

Conjugacy classes & character table

25300 conjugacy classes. The character table is too large to display.

Relationships

automorphism group of	C₂₃×C₁₁₅₁
outer automorphism group of	C₂₃×C₁₁₅₁

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25300, 17);

C22×C11×C23×C25 #38760680