C₂²×C₂₃×C₄₇ #16864474

order	4324
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 6072
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂

Aliases

abelian	C₂²×C₂₃×C₄₇
multiplicative	(ℤ/6627)ˣ, (ℤ/8836)ˣ, (ℤ/13254)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator, Frattini	C₁	G
LCS	G ▷ C₁
UCS	C₁ ◁ G

20 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 74
transitive degree	μ_t(G) = 4324

A minimal faithful permutation representation — 2 generators on 74 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);(3,4)

Conjugacy classes & character table

4324 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂²×C₃×C₂₃×C₄₇, A₄×C₂₃×C₄₇, C₂×D₃×C₂₃×C₄₇, …
maximal normal subgroup of	C₂²×C₃×C₂₃×C₄₇, A₄×C₂₃×C₄₇, C₂²×C₅×C₂₃×C₄₇, …
maximal quotient of	C₂²×C₃×C₂₃×C₄₇, C₂×D₃×C₂₃×C₄₇, C₂²×C₅×C₂₃×C₄₇, …
automorphism group of	C₃×C₂₂₀₉, C₄×C₂₂₀₉
outer automorphism group of	C₃×C₂₂₀₉, C₄×C₂₂₀₉

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4324, 7);

C22×C23×C47 #16864474