C₁₇×#1470 #14524476

order	2176
nilpotency class	3
isoclinism	isoclinic class of #1468
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₇ · Schur multiplier (H₂) = C₂×C₄

Aliases

direct product

C₁₇×#1470

Subgroups

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

204 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 204 conjugacy classes of subgroups — too many to draw. Only its 92 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) = 49
transitive degree	μ_t(G) = 1088

A minimal faithful permutation representation — 3 generators on 49 points:

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

Conjugacy classes & character table

544 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#16926578, #16926588, #16926639, …
maximal subgroup of	C₁₇×#8476, C₁₇×#8478, C₁₇×#8485, …
maximal normal subgroup of	C₁₇×#8476, C₁₇×#8478, C₁₇×#8485, …
maximal quotient of	C₁₇×#7657, C₁₇×#7660, C₁₇×#7663, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 202);