C₁₇×C₂₅×C₃₇ #30628429

order	15725
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	?
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₁₅₇₂₅
abelian	C₁₇×C₂₅×C₃₇

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₅	C₅×C₁₇×C₃₇
socle, prime radical	C₅×C₁₇×C₃₇	C₅
LCS	G ▷ C₁
UCS	C₁ ◁ G

12 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 79
transitive degree	μ_t(G) = 15725

A minimal faithful permutation representation — 1 generator on 79 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)

Conjugacy classes & character table

15725 conjugacy classes. The character table is too large to display.

Relationships

derived subgroup of	D₁₅₇₂₅, Dic₁₅₇₂₅, C₂×D₁₅₇₂₅
Fitting subgroup of	C₁₇×C₂₅×D₃₇, C₂₅×D₁₇×C₃₇, C₂₅×D₆₂₉, …
maximal subgroup of	C₂×C₁₇×C₂₅×C₃₇, C₁₇×C₂₅×D₃₇, C₂₅×D₁₇×C₃₇, …
maximal normal subgroup of	C₂×C₁₇×C₂₅×C₃₇, C₁₇×C₂₅×D₃₇, C₂₅×D₁₇×C₃₇, …
maximal quotient of	C₂×C₁₇×C₂₅×C₃₇

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15725, 1);

C17×C25×C37 #30628429