C₃×C₄×C₇×C₁₃×C₂₅ #41031111

order	27300
nilpotency class	1
automorphism	?
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₂₇₃₀₀
abelian	C₃×C₄×C₇×C₁₃×C₂₅

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂×C₅	C₂×C₃×C₅×C₇×C₁₃
socle, prime radical	C₂×C₃×C₅×C₇×C₁₃	C₂×C₅
LCS	G ▷ C₁
UCS	C₁ ◁ G

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 52
transitive degree	μ_t(G) = 27300

A minimal faithful permutation representation — 1 generator on 52 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)

Conjugacy classes & character table

27300 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of	Dic₁₃₆₅₀, D₂₇₃₀₀
maximal subgroup of	Dic₁₃₆₅₀, D₂₇₃₀₀
maximal normal subgroup of	Dic₁₃₆₅₀, D₂₇₃₀₀

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(27300, 1);

C3×C4×C7×C13×C25 #41031111