C₄×C₂₅×C₄₇ #17989873

order	4700
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) = C₂²×C₄×C₅×C₂₃ (order 1840) · Inn(G) = C₁ · Out(G) = C₂²×C₄×C₅×C₂₃
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₄₇₀₀
abelian	C₄×C₂₅×C₄₇

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂×C₅	C₂×C₅×C₄₇
socle, prime radical	C₂×C₅×C₄₇	C₂×C₅
LCS	G ▷ C₁
UCS	C₁ ◁ G

18 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 76
transitive degree	μ_t(G) = 4700

A minimal faithful permutation representation — 1 generator on 76 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)

Conjugacy classes & character table

4700 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃×C₄×C₂₅×C₄₇, Dic₃×C₂₅×C₄₇, C₄×C₇×C₂₅×C₄₇, …
maximal normal subgroup of	C₃×C₄×C₂₅×C₄₇, C₄×C₇×C₂₅×C₄₇, C₈×C₂₅×C₄₇, …
maximal quotient of	C₃×C₄×C₂₅×C₄₇, Dic₃×C₂₅×C₄₇, C₄×C₇×C₂₅×C₄₇, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4700, 1);

C4×C25×C47 #17989873