C₄×C₁₃×C₁₇×C₁₉ #30680983

order	16796
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	?
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₁₆₇₉₆
abelian	C₄×C₁₃×C₁₇×C₁₉

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂	C₂×C₁₃×C₁₇×C₁₉
socle, prime radical	C₂×C₁₃×C₁₇×C₁₉	C₂
LCS	G ▷ C₁
UCS	C₁ ◁ G

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 53
transitive degree	μ_t(G) = 16796

A minimal faithful permutation representation — 1 generator on 53 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)

Conjugacy classes & character table

16796 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of	Dic₈₃₉₈, D₁₆₇₉₆
maximal subgroup of	Dic₈₃₉₈, D₁₆₇₉₆
maximal normal subgroup of	Dic₈₃₉₈, D₁₆₇₉₆

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16796, 1);

C4×C13×C17×C19 #30680983