C₂×C₁₇×#354 #14525131

order	2176
nilpotency class	4
isoclinism	isoclinic class of #353
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₇ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₂×C₁₇×#354

Subgroups

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

284 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 284 conjugacy classes of subgroups — too many to draw. Only its 88 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) = 35
transitive degree	μ_t(G) = 544

A minimal faithful permutation representation — 3 generators on 35 points:

(1,2)(19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35);(3,4)(5,11,13,18)(6,14,16,9)(7,10)(8,12)(15,17);(3,5,7,13)(4,8,10,17)(6,15,16,12)(9,18,14,11)

Conjugacy classes & character table

442 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#16922050, #16922074, #16922109, …
maximal subgroup of	C₁₇×#7481, C₁₇×#7489, C₁₇×#7502, …
maximal normal subgroup of	C₁₇×#7481, C₁₇×#7489, C₁₇×#7502, …
maximal quotient of	C₂×C₁₇×#1319, C₂×C₁₇×#1324, C₁₇×#11477, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 857);