C₄×C₁₃×C₁₉×C₂₅ #37590757

order	24700
nilpotency class	1
automorphism	?
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₂₄₇₀₀
abelian	C₄×C₁₃×C₁₉×C₂₅

Subgroups

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

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 61
transitive degree	μ_t(G) = 24700

A minimal faithful permutation representation — 1 generator on 61 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)

Conjugacy classes & character table

24700 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of	Dic₁₂₃₅₀, D₂₄₇₀₀
maximal subgroup of	Dic₁₂₃₅₀, D₂₄₇₀₀
maximal normal subgroup of	Dic₁₂₃₅₀, D₂₄₇₀₀

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24700, 1);

C4×C13×C19×C25 #37590757