C₁₇×#12779 #16870523

order	4352
nilpotency class	4
isoclinism	isoclinic class of #12778
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₇ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₁₇×#12779

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₇	#1790
commutator	C₂×Q₈	C₂²×C₄×C₁₇
Frattini, cosocle	C₂×#41	C₂³×C₁₇
prime radical	C₁₇×#532	C₂²
LCS	G ▷ C₂×Q₈ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₇ ◁ C₂×C₄×C₁₇ ◁ C₂×#41×C₁₇ ◁ G

732 conjugacy classes of subgroups; only the 138 normal subgroups are shown.

normal subgroups only

This group has 732 conjugacy classes of subgroups — too many to draw. Only its 138 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)(20,30,33,44)(21,27,22,35)(23,28)(24,29)(25,31)(26,34,43,37)(32,46,49,39)(36,41)(38,42)(40,47)(45,48);(18,20,24,33)(19,25,29,41)(21,31,22,36)(23,32,38,49)(26,39,43,46)(27,44,35,30)(28,45,42,40)(34,47,37,48);(18,21)(19,26)(20,31)(22,24)(23,37)(25,39)(27,42)(28,35)(29,43)(30,45)(32,48)(33,36)(34,38)(40,44)(41,46)(47,49)

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, 5767);