C₁₇×#12509 #16870253

order	4352
nilpotency class	4
isoclinism	isoclinic class of #12503
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₇ · Schur multiplier (H₂) = C₂×C₈

Aliases

direct product

C₁₇×#12509

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₇	#493
commutator, Frattini, cosocle	C₄×C₈	C₂³×C₁₇
prime radical	C₁₇×#1712	C₂
LCS	G ▷ C₄×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₄²×C₁₇ ◁ C₈²×C₁₇ ◁ G

306 conjugacy classes of subgroups; only the 110 normal subgroups are shown.

normal subgroups only

This group has 306 conjugacy classes of subgroups — too many to draw. Only its 110 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)(20,26)(21,29)(22,24)(23,27)(25,30)(28,32)(31,33)(35,42)(36,47)(37,38)(39,40)(43,48)(44,46)(45,49);(18,20,21,27,22,28,30,33)(19,23,25,26,24,31,29,32)(34,35,43,49,39,45,37,42,41,47,38,44,40,46,48,36);(19,24)(23,31)(25,29)(26,32)(34,36,48,46,40,44,38,47,41,42,37,45,39,49,43,35)

Conjugacy classes & character table

1190 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 5497);