C₃×C₄×C₂₅×C₄₃ #27166332

order	12900
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	?
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₁₂₉₀₀
abelian	C₃×C₄×C₂₅×C₄₃

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂×C₅	C₂×C₃×C₅×C₄₃
socle, prime radical	C₂×C₃×C₅×C₄₃	C₂×C₅
LCS	G ▷ C₁
UCS	C₁ ◁ G

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 75
transitive degree	μ_t(G) = 12900

A minimal faithful permutation representation — 1 generator on 75 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)

Conjugacy classes & character table

12900 conjugacy classes. The character table is too large to display.

Relationships

derived subgroup of	Dic₁₂₉₀₀, D₂₅₈₀₀
Fitting subgroup of	D₁₂₉₀₀, Dic₆₄₅₀
maximal subgroup of	C₃×C₈×C₂₅×C₄₃, C₂×C₃×C₄×C₂₅×C₄₃, D₁₂₉₀₀, …
maximal normal subgroup of	C₃×C₈×C₂₅×C₄₃, C₂×C₃×C₄×C₂₅×C₄₃, D₁₂₉₀₀, …
maximal quotient of	C₃×C₈×C₂₅×C₄₃, C₂×C₃×C₄×C₂₅×C₄₃

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12900, 1);

C3×C4×C25×C43 #27166332