C₃×C₇×C₂₅×C₆₁ #44545045

order	32025
nilpotency class	1
automorphism	?
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₃₂₀₂₅
abelian	C₃×C₇×C₂₅×C₆₁

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₅	C₃×C₅×C₇×C₆₁
socle, prime radical	C₃×C₅×C₇×C₆₁	C₅
LCS	G ▷ C₁
UCS	C₁ ◁ G

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 96
transitive degree	μ_t(G) = 32025

A minimal faithful permutation representation — 1 generator on 96 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)(36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96)

Conjugacy classes & character table

32025 conjugacy classes. The character table is too large to display.

Relationships

derived subgroup of	D₃₂₀₂₅
Fitting subgroup of	D₃₂₀₂₅
maximal subgroup of	D₃₂₀₂₅
maximal normal subgroup of	D₃₂₀₂₅

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32025, 1);

C3×C7×C25×C61 #44545045