C₁₇×#2212 #14525218

order	2176
nilpotency class	4
isoclinism	isoclinic class of #2212
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₇ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₇×#2212

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₇	#459
commutator, Frattini, cosocle	C₂×C₈	C₂³×C₁₇
prime radical	C₁₇×#509	C₂
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₇ ◁ C₂×C₄×C₁₇ ◁ C₄×C₈×C₁₇ ◁ G

154 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 154 conjugacy classes of subgroups — too many to draw. Only its 60 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)(20,28)(21,33)(22,37)(23,39)(24,29)(25,31)(26,30)(27,38)(32,46)(34,45)(35,49)(36,41)(40,42)(43,47)(44,48);(18,20,22,31,24,32,38,23)(19,25,27,28,29,39,37,46)(21,30,34,47,36,48,35,40)(26,41,42,45,44,33,43,49);(18,21)(19,26)(20,30)(22,34)(23,40)(24,36)(25,41)(27,42)(28,45)(29,44)(31,47)(32,48)(33,39)(35,38)(37,43)(46,49)

Conjugacy classes & character table

391 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	D₁₇×#2212, #17188712, #17188720, …
maximal subgroup of	C₂×C₁₇×#2212, C₁₇×#33594, C₁₇×#33595, …
maximal normal subgroup of	C₂×C₁₇×#2212, C₁₇×#33594, C₁₇×#33595, …
maximal quotient of	C₁₇×#12416, C₁₇×#12417, C₁₇×#12420, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 944);