C₂×C₁₁×C₂₅×C₅₉ #44570078

order	32450
nilpotency class	1
automorphism	?
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₃₂₄₅₀
abelian	C₂×C₁₁×C₂₅×C₅₉

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₅	C₂×C₅×C₁₁×C₅₉
socle, prime radical	C₂×C₅×C₁₁×C₅₉	C₅
LCS	G ▷ C₁
UCS	C₁ ◁ G

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 97
transitive degree	μ_t(G) = 32450

A minimal faithful permutation representation — 1 generator on 97 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)(39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97)

Conjugacy classes & character table

32450 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of	Dic₁₆₂₂₅, C₂×D₁₆₂₂₅
maximal subgroup of	Dic₁₆₂₂₅, C₂×D₁₆₂₂₅
maximal normal subgroup of	Dic₁₆₂₂₅, C₂×D₁₆₂₂₅

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32450, 1);

C2×C11×C25×C59 #44570078