C₁₇×#2047 #14525053

order	2176
nilpotency class	3
isoclinism	isoclinic class of #2018
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₇ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₇×#2047

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₇	#121
commutator, Frattini, cosocle	C₂²×C₄	C₂³×C₁₇
prime radical	C₂³×C₁₇	#41
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₂²×C₄×C₁₇ ◁ G

256 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 256 conjugacy classes of subgroups — too many to draw. Only its 84 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 — 3 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)(22,23,27,31)(24,32,35,47)(25,36,39,29)(26,40,42,30)(28,41,44,34)(33,49,37,48)(38,46,53,51)(43,50,45,52);(22,24,27,35)(23,28,31,44)(25,37,39,33)(26,41,42,34)(29,45,36,43)(30,47,40,32)(38,50,53,52)(46,48,51,49);(19,21)(22,25,26,38,27,39,42,53)(23,29,30,46,31,36,40,51)(24,33,34,50,35,37,41,52)(28,43,32,48,44,45,47,49)

Conjugacy classes & character table

442 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#16946815, #16946820, #16946825, …
maximal subgroup of	C₁₇×#12167, C₁₇×#12168, C₁₇×#12169, …
maximal normal subgroup of	C₁₇×#12167, C₁₇×#12168, C₁₇×#12169, …
maximal quotient of	C₁₇×#10446, C₁₇×#10447, C₁₇×#10454, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 779);