C₂²×C₃²×C₁₉×C₂₅ #30685456

order	17100
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	?
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂×C₃

Aliases

abelian	C₂²×C₃²×C₁₉×C₂₅
multiplicative	(ℤ/19957)ˣ, (ℤ/25659)ˣ, (ℤ/39914)ˣ, (ℤ/51318)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₅	C₂²×C₃²×C₅×C₁₉
socle, prime radical	C₂²×C₃²×C₅×C₁₉	C₅
LCS	G ▷ C₁
UCS	C₁ ◁ G

180 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 54
transitive degree	μ_t(G) = 17100

A minimal faithful permutation representation — 2 generators on 54 points:

(1,2)(5,6,7)(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);(3,4)(8,9,10)

Conjugacy classes & character table

17100 conjugacy classes. The character table is too large to display.

Relationships

automorphism group of	C₇×C₂₈₅₁
outer automorphism group of	C₇×C₂₈₅₁

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17100, 93);

C22×C32×C19×C25 #30685456