C₁₇×#7248 #16864992

order	4352
nilpotency class	4
isoclinism	isoclinic class of #7213
automorphism	?
homology	Abelianization (H₁) = C₄²×C₁₇ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₇×#7248

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₇	#342
commutator	C₂²×C₄	C₄²×C₁₇
Frattini, cosocle	C₂×C₄×Q₈	C₂²×C₁₇
prime radical	C₂³×C₁₇	#95
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₂²×C₄×C₁₇ ◁ C₂×C₄×Q₈×C₁₇ ◁ G

244 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 244 conjugacy classes of subgroups — too many to draw. Only its 78 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) = 2176

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)(18,19,21,26,23,27,22,25)(20,28,29,24,31,32,30,33)(34,35,37,41,38,42,46,49)(36,40,43,48,44,39,45,47);(18,20,22,30,23,31,21,29)(19,24,26,32,27,33,25,28)(35,39,42,40)(41,48,49,47)

Conjugacy classes & character table

680 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 236);