C₁₇×#1552 #14524558

order	2176
nilpotency class	3
isoclinism	isoclinic class of #1504
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₇ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₇×#1552

Subgroups

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

208 conjugacy classes of subgroups; only the 96 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 96 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 — 3 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)(26,27,29,33,30,32,38,40)(28,34,35,41,36,31,37,39);(18,19,22,24)(20,23,21,25)(26,28,30,36)(27,31,32,34)(29,37,38,35)(33,41,40,39);(18,20,22,21)(19,23,24,25)(27,32)(31,34)(33,40)(39,41)

Conjugacy classes & character table

544 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#16926471, #16926479, #16926488, …
maximal subgroup of	C₁₇×#8457, C₁₇×#8458, C₁₇×#8460, …
maximal normal subgroup of	C₁₇×#8457, C₁₇×#8458, C₁₇×#8460, …
maximal quotient of	C₁₇×#7579, C₁₇×#7585, C₁₇×#7613, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 284);