C₁₇×#1301 #14524307

order	2176
nilpotency class	3
isoclinism	isoclinic class of #327
automorphism	?
homology	Abelianization (H₁) = C₄²×C₁₇ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₇×#1301

Subgroups

	subgroup	G/H
center	C₂×C₄×C₁₇	C₂²⋊C₄
commutator	C₂×C₄	C₄²×C₁₇
Frattini, cosocle	C₂×C₄²	C₂²×C₁₇
socle	C₂²×C₁₇	#95
prime radical	C₂³×C₁₇	C₄⋊C₄
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₇ ◁ C₂×C₄²×C₁₇ ◁ G

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

normal subgroups only

This group has 148 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) = 41
transitive degree	μ_t(G) = 1088

A minimal faithful permutation representation — 2 generators on 41 points:

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

Conjugacy classes & character table

646 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	D₁₇×#1301, #16924550, #16924554, …
maximal subgroup of	C₂×C₁₇×#1301, C₁₇×#8076, C₁₇×#8077, …
maximal normal subgroup of	C₂×C₁₇×#1301, C₁₇×#8076, C₁₇×#8077, …
maximal quotient of	C₁₇×#7027, C₁₇×#7029, C₁₇×#7031, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 33);