C₄×C₁₇×C₁₉×C₂₅ #44568012

order	32300
nilpotency class	1
automorphism	?
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₃₂₃₀₀
abelian	C₄×C₁₇×C₁₉×C₂₅

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂×C₅	C₂×C₅×C₁₇×C₁₉
socle, prime radical	C₂×C₅×C₁₇×C₁₉	C₂×C₅
LCS	G ▷ C₁
UCS	C₁ ◁ G

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 65
transitive degree	μ_t(G) = 32300

A minimal faithful permutation representation — 1 generator on 65 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)

Conjugacy classes & character table

32300 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of	Dic₁₆₁₅₀, D₃₂₃₀₀
maximal subgroup of	Dic₁₆₁₅₀, D₃₂₃₀₀
maximal normal subgroup of	Dic₁₆₁₅₀, D₃₂₃₀₀

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32300, 1);

C4×C17×C19×C25 #44568012