C₂×C₁₃×C₁₉×C₂₅ #27134690

order	12350
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 4320
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₁₂₃₅₀
abelian	C₂×C₁₃×C₁₉×C₂₅

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₅	C₂×C₅×C₁₃×C₁₉
socle, prime radical	C₂×C₅×C₁₃×C₁₉	C₅
LCS	G ▷ C₁
UCS	C₁ ◁ G

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 59
transitive degree	μ_t(G) = 12350

A minimal faithful permutation representation — 1 generator on 59 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)

Conjugacy classes & character table

12350 conjugacy classes. The character table is too large to display.

Relationships

derived subgroup of	Dic₁₂₃₅₀, D₂₄₇₀₀
Fitting subgroup of	C₁₃×C₂₅×Dic₁₉, C₁₉×C₂₅×Dic₁₃, C₂₅×Dic₂₄₇, …
maximal subgroup of	C₄×C₁₃×C₁₉×C₂₅, C₁₃×C₂₅×Dic₁₉, C₁₉×C₂₅×Dic₁₃, …
maximal normal subgroup of	C₄×C₁₃×C₁₉×C₂₅, C₁₃×C₂₅×Dic₁₉, C₁₉×C₂₅×Dic₁₃, …
maximal quotient of	C₄×C₁₃×C₁₉×C₂₅, C₂²×C₁₃×C₁₉×C₂₅, C₂×C₃×C₁₃×C₁₉×C₂₅, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12350, 1);

C2×C13×C19×C25 #27134690