C₁₇×#1382 #14524388

order	2176
nilpotency class	4
isoclinism	isoclinic class of D₁₆
automorphism	?
homology	Abelianization (H₁) = C₄²×C₁₇ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₇×#1382

Subgroups

	subgroup	G/H
center	C₂×C₄×C₁₇	D₈
commutator	C₈	C₄²×C₁₇
Frattini, cosocle	C₂²×C₈	C₂²×C₁₇
socle	C₂²×C₁₇	#102
prime radical	C₂³×C₁₇	SD₁₆
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₇ ◁ C₂²×C₄×C₁₇ ◁ C₂²×C₈×C₁₇ ◁ G

132 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 132 conjugacy classes of subgroups — too many to draw. Only its 80 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) = 53
transitive degree	μ_t(G) = 1088

A minimal faithful permutation representation — 2 generators on 53 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19,20,21)(22,23)(24,33)(25,38)(26,41)(27,43)(28,32)(29,34)(30,40)(31,39)(35,45)(36,53)(37,49)(42,46)(44,52)(47,51)(48,50);(22,24,26,35,39,50,40,51,28,37,25,34,27,36,42,52)(23,29,30,33,43,47,41,53,32,45,46,49,31,44,38,48)

Conjugacy classes & character table

748 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	D₁₇×#1382, #16949219, #16949547, …
maximal subgroup of	C₂×C₁₇×#1382, C₁₇×#12561, C₄×C₁₇×#359, …
maximal normal subgroup of	C₂×C₁₇×#1382, C₁₇×#12561, C₄×C₁₇×#359, …
maximal quotient of	C₁₇×#7155, C₁₇×#7171, C₁₇×#7172, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 114);