C₁₇×#19006 #16876750

order	4352
nilpotency class	3
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₇ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₁₇×#19006

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₇	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₇
prime radical	C₂×C₁₇×#562	C₂
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₂×C₄²×C₁₇ ◁ G

938 conjugacy classes of subgroups; only the 222 normal subgroups are shown.

normal subgroups only

This group has 938 conjugacy classes of subgroups — too many to draw. Only its 222 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) = 1088

A minimal faithful permutation representation — 4 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)(21,27)(22,26)(23,25)(24,29)(30,33)(31,32)(34,35,38,40)(36,42,44,49)(37,45,47,41)(39,46,48,43);(18,20)(19,24)(21,31)(22,29)(23,30)(25,32)(26,33)(27,28)(34,36,38,44)(35,39,40,48)(37,46,47,43)(41,49,45,42);(18,20)(19,24)(21,29)(22,31)(23,30)(25,32)(26,28)(27,33)(37,47)(41,45)(42,49)(43,46);(19,25)(24,32)(26,27)(28,33)(35,40)(39,48)(41,45)(42,49)

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, 11994);