C₁₇×#11912 #16869656

order	4352
nilpotency class	4
isoclinism	isoclinic class of #11912
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₇ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₇×#11912

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₇	#1530
commutator	C₄²	C₂²×C₄×C₁₇
Frattini, cosocle	#97	C₂³×C₁₇
prime radical	C₁₇×#540	C₄
LCS	G ▷ C₄² ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₇ ◁ C₂×C₄×C₁₇ ◁ C₁₇×#405 ◁ G

284 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 284 conjugacy classes of subgroups — too many to draw. Only its 94 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)(18,19,21,27,22,24,36,38,23,28,35,44,37,26,33,43)(20,29,31,46,32,41,48,45,30,42,34,49,47,25,39,40);(19,24)(21,33)(22,37)(25,29)(26,28)(27,44)(31,39)(32,47)(34,48)(35,36)(40,45)(41,42);(18,20)(19,25,28,41)(21,34)(22,32)(23,30)(24,29,26,42)(27,45,44,40)(31,35)(33,48)(36,39)(37,47)(38,49,43,46)

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, 4900);