C₁₇×#12708 #16870452

order	4352
nilpotency class	4
isoclinism	isoclinic class of #12707
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₇ · Schur multiplier (H₂) = C₂⁶

Aliases

direct product

C₁₇×#12708

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₇	#1781
commutator	C₂²×C₄	C₂²×C₄×C₁₇
Frattini, cosocle	C₂²×D₄	C₂³×C₁₇
prime radical	C₁₇×#3487	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₇ ◁ C₂³×C₁₇ ◁ C₂²×#41×C₁₇ ◁ G

1002 conjugacy classes of subgroups; only the 146 normal subgroups are shown.

normal subgroups only

This group has 1002 conjugacy classes of subgroups — too many to draw. Only its 146 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) = 544

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

Conjugacy classes & character table

578 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 5696);