C₁₇×#1556 #14524562

order	2176
nilpotency class	3
isoclinism	isoclinic class of #1510
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₇ · Schur multiplier (H₂) = C₂×C₄

Aliases

direct product

C₁₇×#1556

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

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

normal subgroups only

This group has 228 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)(18,19,21,23,22,24,20,25)(26,27,29,33,30,32,38,40)(28,34,35,41,36,31,37,39);(19,23)(20,21)(24,25)(26,28,30,36)(27,31,32,34)(29,37,38,35)(33,41,40,39);(19,24)(23,25)

Conjugacy classes & character table

442 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#16926725, #16926847, #16926856, …
maximal subgroup of	C₁₇×#8499, C₁₇×#8523, C₁₇×#8525, …
maximal normal subgroup of	C₁₇×#8499, C₁₇×#8523, C₁₇×#8525, …
maximal quotient of	C₁₇×#7593, C₁₇×#7604, C₁₇×#7627, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 288);