C₁₇×#2221 #14525227

order	2176
nilpotency class	4
isoclinism	isoclinic class of #2221
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₇ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₇×#2221

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₇	#466
commutator, Frattini, cosocle	C₂×C₈	C₂³×C₁₇
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₇ ◁ C₂×C₄×C₁₇ ◁ C₁₇×#131 ◁ G

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

normal subgroups only

This group has 148 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)(19,25)(20,31)(21,26)(22,23)(27,42)(28,39)(29,38)(30,40)(32,46)(33,36)(34,35)(37,43)(44,49)(45,48);(18,19,26,39,23,29,35,40,24,30,34,38,22,28,21,25)(20,27,41,42,31,43,46,48,33,44,47,49,36,45,32,37);(18,20)(19,27)(21,32)(22,36)(23,31)(24,33)(25,37)(26,41)(28,45)(29,43)(30,44)(34,47)(35,46)(38,49)(39,42)(40,48)

Conjugacy classes & character table

442 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#16955006, #16955013, #16955187, …
maximal subgroup of	C₁₇×#13669, C₁₇×#13670, C₁₇×#13700, …
maximal normal subgroup of	C₁₇×#13669, C₁₇×#13670, C₁₇×#13700, …
maximal quotient of	C₁₇×#12430, C₁₇×#12433, C₁₇×#12439, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 953);