C₁₉×C₂₅×C₃₇ #31798407

order	17575
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	?
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₁₇₅₇₅
abelian	C₁₉×C₂₅×C₃₇

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₅	C₅×C₁₉×C₃₇
socle, prime radical	C₅×C₁₉×C₃₇	C₅
LCS	G ▷ C₁
UCS	C₁ ◁ G

12 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 81
transitive degree	μ_t(G) = 17575

A minimal faithful permutation representation — 1 generator on 81 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)(45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81)

Conjugacy classes & character table

17575 conjugacy classes. The character table is too large to display.

Relationships

derived subgroup of	D₁₇₅₇₅
Fitting subgroup of	C₁₉×C₂₅×D₃₇, C₂₅×C₃₇×D₁₉, C₂₅×D₇₀₃, …
maximal subgroup of	C₂×C₁₉×C₂₅×C₃₇, C₁₉×C₂₅×D₃₇, C₂₅×C₃₇×D₁₉, …
maximal normal subgroup of	C₂×C₁₉×C₂₅×C₃₇, C₁₉×C₂₅×D₃₇, C₂₅×C₃₇×D₁₉, …
maximal quotient of	C₂×C₁₉×C₂₅×C₃₇

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17575, 1);

C19×C25×C37 #31798407