C₁₇×#7040 #16864784

order	4352
nilpotency class	3
isoclinism	isoclinic class of #7035
automorphism	?
homology	Abelianization (H₁) = C₄²×C₁₇ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₇×#7040

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂³×C₁₇	#95
commutator	C₂²×C₄	C₄²×C₁₇
Frattini, cosocle	C₄³	C₂²×C₁₇
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₇ ◁ C₄³×C₁₇ ◁ G

292 conjugacy classes of subgroups; only the 138 normal subgroups are shown.

normal subgroups only

This group has 292 conjugacy classes of subgroups — too many to draw. Only its 138 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) = 49
transitive degree	μ_t(G) = 4352

A minimal faithful permutation representation — 2 generators on 49 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(19,23)(20,21)(24,25)(26,27,29,31,30,33,28,32)(34,35,37,40,38,41,45,48)(36,42,44,49,43,39,46,47);(18,19,21,24,22,25,20,23)(27,31)(28,29)(32,33)(34,36)(35,39,41,42)(37,44)(38,43)(40,47,48,49)(45,46)

Conjugacy classes & character table

884 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 28);