C₂×C₃×C₁₁×C₁₉×C₂₅ #44535428

order	31350
nilpotency class	1
automorphism	?
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₃₁₃₅₀
abelian	C₂×C₃×C₁₁×C₁₉×C₂₅

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₅	C₂×C₃×C₅×C₁₁×C₁₉
socle, prime radical	C₂×C₃×C₅×C₁₁×C₁₉	C₅
LCS	G ▷ C₁
UCS	C₁ ◁ G

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 60
transitive degree	μ_t(G) = 31350

A minimal faithful permutation representation — 1 generator on 60 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)

Conjugacy classes & character table

31350 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of	Dic₁₅₆₇₅, C₂×D₁₅₆₇₅
maximal subgroup of	Dic₁₅₆₇₅, C₂×D₁₅₆₇₅
maximal normal subgroup of	Dic₁₅₆₇₅, C₂×D₁₅₆₇₅

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31350, 1);

C2×C3×C11×C19×C25 #44535428