C₇×#13660 #13190876

order	1792
nilpotency class	2
isoclinism	isoclinic class of #120
automorphism	?
homology	Abelianization (H₁) = C₂²×C₇×C₁₆ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₇×#13660

Subgroups

	subgroup	G/H
center	C₂×C₇×C₁₆	C₂³
commutator	C₂²	C₂²×C₇×C₁₆
Frattini, cosocle	C₂×C₁₆	C₂³×C₇
socle, prime radical	C₂²×C₇	C₂²×C₁₆
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₇×C₁₆ ◁ G

158 conjugacy classes of subgroups; only the 126 normal subgroups are shown.

normal subgroups only

This group has 158 conjugacy classes of subgroups — too many to draw. Only its 126 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

minimal degree	μ(G) = 47
transitive degree	μ_t(G) = 1792

A minimal faithful permutation representation — 3 generators on 47 points:

(1,2,3,4,5,6,7)(8,9)(10,15)(11,13)(12,14)(16,17,19,24,20,25,31,39,21,18,27,28,33,29,42,43,22,26,32,40,34,41,45,47,35,30,23,36,37,44,38,46);(8,10,12,11)(9,13,14,15);(8,11,12,10)(9,13,14,15)(16,18,19,28,20,29,31,43,21,26,27,40,33,41,42,47,22,30,32,36,34,44,45,46,35,17,23,24,37,25,38,39)

Conjugacy classes & character table

784 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1792, 6648);