C₁₇×#2049 #14525055

order	2176
nilpotency class	3
isoclinism	isoclinic class of #2048
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₇ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₇×#2049

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₇	#394
commutator, Frattini, cosocle	C₂²×C₄	C₂³×C₁₇
prime radical	C₂×#41×C₁₇	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₇ ◁ C₂²×C₄×C₁₇ ◁ G

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

normal subgroups only

This group has 254 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) = 49
transitive degree	μ_t(G) = 544

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)(18,19,24,29)(20,30,33,45)(21,34,38,43)(22,28,23,27)(25,39,41,32)(26,36,44,37)(31,42,35,40)(46,49,48,47);(18,20)(19,25)(21,35)(22,39)(23,32)(24,33)(26,42)(27,45)(28,30)(29,41)(31,38)(34,48)(36,47)(37,49)(40,44)(43,46);(18,21,22,36,24,38,23,37)(19,26,27,43,29,44,28,34)(20,31,32,47,33,35,39,49)(25,40,30,46,41,42,45,48)

Conjugacy classes & character table

391 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	D₁₇×#2049, #17062171, #17070345, …
maximal subgroup of	C₂×C₁₇×#2049, C₁₇×#23525, C₁₇×#24295, …
maximal normal subgroup of	C₂×C₁₇×#2049, C₁₇×#23525, C₁₇×#24295, …
maximal quotient of	C₁₇×#10444, C₁₇×#10445, C₁₇×#10446, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 781);