C₁₇×#2240 #14525246

order	2176
nilpotency class	4
isoclinism	isoclinic class of #2215
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₇ · Schur multiplier (H₂) = C₂×C₄

Aliases

direct product

C₁₇×#2240

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₇	C₂×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂³×C₁₇
prime radical	C₁₇×#493	C₂
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₄²×C₁₇ ◁ C₄×C₈×C₁₇ ◁ G

160 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 160 conjugacy classes of subgroups — too many to draw. Only its 72 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)(20,23)(21,22)(24,25)(27,33)(28,38)(29,40)(30,41)(31,34)(35,36)(37,39);(19,22)(23,25)(26,27,30,35,31,36,29,33,32,37,40,28,34,38,41,39);(18,20,21,24)(19,23,22,25)(26,28,29,27,34,33,30,38,32,35,41,37,31,39,40,36)

Conjugacy classes & character table

646 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#16947913, #16947920, #16947927, …
maximal subgroup of	C₁₇×#12340, C₁₇×#12341, C₁₇×#12342, …
maximal normal subgroup of	C₁₇×#12340, C₁₇×#12341, C₁₇×#12342, …
maximal quotient of	C₁₇×#12888, C₁₇×#13147, C₁₇×#13202, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 972);