C₁₇×#11652 #16869396

order	4352
nilpotency class	4
isoclinism	isoclinic class of #11651
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₇ · Schur multiplier (H₂) = C₂×C₄

Aliases

direct product

C₁₇×#11652

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₇	C₂×#102
commutator	C₂×C₈	C₂²×C₄×C₁₇
Frattini, cosocle	C₄×C₈	C₂³×C₁₇
prime radical	C₁₇×#3169	C₂
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₂×C₄²×C₁₇ ◁ C₂×C₄×C₈×C₁₇ ◁ G

344 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 344 conjugacy classes of subgroups — too many to draw. Only its 118 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 — 3 generators on 49 points:

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

Conjugacy classes & character table

782 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 4640);