C₁₇×#2122 #14525128

order	2176
nilpotency class	4
isoclinism	isoclinic class of #2121
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₇ · Schur multiplier (H₂) = C₂²×C₄

Aliases

direct product

C₁₇×#2122

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₇	C₂×#99
commutator	C₂³	C₂²×C₄×C₁₇
Frattini, cosocle	C₂×D₄	C₂³×C₁₇
prime radical	C₁₇×#535	C₂
LCS	G ▷ C₂³ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₇ ◁ C₂×C₄×C₁₇ ◁ C₂×#41×C₁₇ ◁ G

266 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 266 conjugacy classes of subgroups — too many to draw. Only its 84 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) = 33
transitive degree	μ_t(G) = 272

A minimal faithful permutation representation — 3 generators on 33 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19)(20,24)(21,28,29,23)(22,25)(26,32)(27,31,33,30);(19,23)(20,26)(24,31)(25,28)(27,33)(30,32);(18,20,22,26)(19,24,25,32)(21,27,29,33)(23,30,28,31)

Conjugacy classes & character table

391 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#16949890, #16949905, #16949918, …
maximal subgroup of	C₁₇×#12715, C₁₇×#12718, C₁₇×#12721, …
maximal normal subgroup of	C₁₇×#12715, C₁₇×#12718, C₁₇×#12721, …
maximal quotient of	C₁₇×#11427, C₁₇×#11454, C₁₇×#11473, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 854);