C₄×C₉×C₁₇×C₄₇ #43273308

order	28764
nilpotency class	1
automorphism	?
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₂₈₇₆₄
abelian	C₄×C₉×C₁₇×C₄₇

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂×C₃	C₂×C₃×C₁₇×C₄₇
socle, prime radical	C₂×C₃×C₁₇×C₄₇	C₂×C₃
LCS	G ▷ C₁
UCS	C₁ ◁ G

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 77
transitive degree	μ_t(G) = 28764

A minimal faithful permutation representation — 1 generator on 77 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)(31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77)

Conjugacy classes & character table

28764 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of	Dic₁₄₃₈₂, D₂₈₇₆₄
maximal subgroup of	Dic₁₄₃₈₂, D₂₈₇₆₄
maximal normal subgroup of	Dic₁₄₃₈₂, D₂₈₇₆₄

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(28764, 1);

C4×C9×C17×C47 #43273308