C₁₇×#3293 #14526299

order	2176
nilpotency class	3
isoclinism	isoclinic class of #3290
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₇ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₁₇×#3293

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₇	D₄²
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₁₇
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₇ ◁ C₂×C₄×C₁₇ ◁ G

444 conjugacy classes of subgroups; only the 184 normal subgroups are shown.

normal subgroups only

This group has 444 conjugacy classes of subgroups — too many to draw. Only its 184 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)(18,19,25,30)(20,31,34,36)(21,33,26,40)(22,27,39,45)(23,29,24,28)(32,47,49,43)(35,48,42,37)(38,46,41,44);(18,20,25,34)(19,26,30,21)(22,37,39,48)(23,40,24,33)(27,43,45,47)(28,36,29,31)(32,41,49,38)(35,44,42,46);(18,21,25,26)(19,20,30,34)(22,35,39,42)(23,36,24,31)(27,32,45,49)(28,33,29,40)(37,46,48,44)(38,47,41,43);(18,22)(19,27)(20,32)(21,35)(23,41)(24,38)(25,39)(26,42)(28,46)(29,44)(30,45)(31,47)(33,48)(34,49)(36,43)(37,40)

Conjugacy classes & character table

493 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#16947722, #16947732, #16948098, …
maximal subgroup of	C₁₇×#12311, C₁₇×#12313, C₁₇×#12367, …
maximal normal subgroup of	C₁₇×#12311, C₁₇×#12313, C₁₇×#12367, …
maximal quotient of	C₁₇×#19887, C₁₇×#19894, C₁₇×#19902, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 2025);