C₄×C₁₁×C₂₃×C₂₅ #38760664

order	25300
nilpotency class	1
automorphism	?
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₂₅₃₀₀
abelian	C₄×C₁₁×C₂₃×C₂₅
multiplicative	(ℤ/25301)ˣ, (ℤ/50602)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂×C₅	C₂×C₅×C₁₁×C₂₃
socle, prime radical	C₂×C₅×C₁₁×C₂₃	C₂×C₅
LCS	G ▷ C₁
UCS	C₁ ◁ G

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

A minimal faithful permutation representation — 1 generator on 63 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)

Conjugacy classes & character table

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

Relationships

Fitting subgroup of	Dic₁₂₆₅₀, D₂₅₃₀₀
maximal subgroup of	Dic₁₂₆₅₀, D₂₅₃₀₀
maximal normal subgroup of	Dic₁₂₆₅₀, D₂₅₃₀₀
automorphism group of	C₂₅₃₀₁
outer automorphism group of	C₂₅₃₀₁

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25300, 1);

C4×C11×C23×C25 #38760664