C₄×C₁₃×C₁₉×C₂₃ #36384334

order	22724
nilpotency class	1
automorphism	?
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₂₂₇₂₄
abelian	C₄×C₁₃×C₁₉×C₂₃

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂	C₂×C₁₃×C₁₉×C₂₃
socle, prime radical	C₂×C₁₃×C₁₉×C₂₃	C₂
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) = 22724

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

22724 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of	Dic₁₁₃₆₂, D₂₂₇₂₄
maximal subgroup of	Dic₁₁₃₆₂, D₂₂₇₂₄
maximal normal subgroup of	Dic₁₁₃₆₂, D₂₂₇₂₄

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22724, 1);

C4×C13×C19×C23 #36384334