C₁₇×#3416 #14526422

order	2176
nilpotency class	4
isoclinism	isoclinic class of #3415
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₇ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₁₇×#3416

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₇	C₂²×D₈
commutator, Frattini, cosocle	C₈	C₂⁴×C₁₇
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₇ ◁ #41×C₁₇ ◁ C₁₇×#131 ◁ G

360 conjugacy classes of subgroups; only the 180 normal subgroups are shown.

normal subgroups only

This group has 360 conjugacy classes of subgroups — too many to draw. Only its 180 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 — 4 generators on 49 points:

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

Conjugacy classes & character table

544 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#17191064, #17191085, #17191094, …
maximal subgroup of	C₁₇×#33854, C₁₇×#33855, C₁₇×#33856, …
maximal normal subgroup of	C₁₇×#33854, C₁₇×#33855, C₁₇×#33856, …
maximal quotient of	C₁₇×#33381, C₁₇×#33382, C₁₇×#33411, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 2148);