C₁₇×#2921 #14525927

order	2176
nilpotency class	2
isoclinism	isoclinic class of #534
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄×C₁₇ · Schur multiplier (H₂) = C₂³×C₄

Aliases

direct product

C₁₇×#2921

Subgroups

	subgroup	G/H
center	C₂×C₄×C₁₇	C₂⁴
commutator	C₂²	C₂³×C₄×C₁₇
Frattini, cosocle	C₂×C₄	C₂⁴×C₁₇
socle	C₂²×C₁₇	C₂³×C₄
prime radical	C₂⁴×C₁₇	C₂×C₄
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₇ ◁ G

392 conjugacy classes of subgroups; only the 264 normal subgroups are shown.

normal subgroups only

This group has 392 conjugacy classes of subgroups — too many to draw. Only its 264 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) = 41
transitive degree	μ_t(G) = 544

A minimal faithful permutation representation — 4 generators on 41 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19)(20,23)(21,22)(24,25)(26,27,29,33,30,32,36,39)(28,31,35,38,34,37,40,41);(19,22)(23,25)(26,28)(27,31)(29,35)(30,34)(32,37)(33,38)(36,40)(39,41);(18,20,21,24)(19,23,22,25)(28,34)(31,37)(35,40)(38,41);(27,32)(31,37)(33,39)(38,41)

Conjugacy classes & character table

748 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#16928355, #16929418, #16929428, …
maximal subgroup of	C₁₇×#8863, C₁₇×#9034, C₁₇×#9036, …
maximal normal subgroup of	C₁₇×#8863, C₁₇×#9034, C₁₇×#9036, …
maximal quotient of	C₁₇×#20365, C₁₇×#20377, C₁₇×#20429, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 1653);