C₁₇×#1735 #14524741

order	2176
nilpotency class	3
isoclinism	isoclinic class of D₈
automorphism	?
homology	Abelianization (H₁) = C₂×C₄²×C₁₇ · Schur multiplier (H₂) = C₂³×C₄

Aliases

direct product

C₁₇×#1735

Subgroups

	subgroup	G/H
center	C₂²×C₄×C₁₇	D₄
commutator	C₄	C₂×C₄²×C₁₇
Frattini, cosocle	C₂²×C₄	C₂³×C₁₇
socle	C₂³×C₁₇	C₂×D₄
prime radical	C₂⁴×C₁₇	D₄
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₇ ◁ C₂³×C₄×C₁₇ ◁ G

424 conjugacy classes of subgroups; only the 232 normal subgroups are shown.

normal subgroups only

This group has 424 conjugacy classes of subgroups — too many to draw. Only its 232 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)(20,21)(22,23,24,25)(26,27)(28,36)(29,33)(30,34)(31,35)(32,37)(38,41)(39,40);(19,21)(26,28,30,38,31,39,29,37)(27,32,33,40,35,41,34,36);(26,29,31,30)(27,33,35,34)(28,37,39,38)(32,40,41,36)

Conjugacy classes & character table

952 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#16921474, #16921480, #16939517, …
maximal subgroup of	C₁₇×#7260, C₁₇×#7262, C₁₇×#10706, …
maximal normal subgroup of	C₁₇×#7260, C₁₇×#7262, C₁₇×#10706, …
maximal quotient of	C₁₇×#7872, C₁₇×#7875, C₁₇×#7878, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 467);