C₇²×C₁₃×C₂₅ #30629936

order	15925
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	?
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₇

Aliases

abelian

C₇²×C₁₃×C₂₅

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₅	C₅×C₇²×C₁₃
socle, prime radical	C₅×C₇²×C₁₃	C₅
LCS	G ▷ C₁
UCS	C₁ ◁ G

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 52
transitive degree	μ_t(G) = 15925

A minimal faithful permutation representation — 2 generators on 52 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)(40,41,42,43,44,45,46,47,48,49,50,51,52);(33,34,35,36,37,38,39)

Conjugacy classes & character table

15925 conjugacy classes. The character table is too large to display.

Relationships

derived subgroup of	C₇⋊D₂₂₇₅
Fitting subgroup of	C₇²×C₂₅×D₁₃, C₇×C₁₃×D₇×C₂₅, C₇×C₂₅×D₉₁, …
maximal subgroup of	C₂×C₇²×C₁₃×C₂₅, C₇²×C₂₅×D₁₃, C₇×C₁₃×D₇×C₂₅, …
maximal normal subgroup of	C₂×C₇²×C₁₃×C₂₅, C₇²×C₂₅×D₁₃, C₇×C₁₃×D₇×C₂₅, …
maximal quotient of	C₂×C₇²×C₁₃×C₂₅

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15925, 3);

C72×C13×C25 #30629936