C₁₇×#2195 #14525201

order	2176
nilpotency class	4
isoclinism	isoclinic class of #2192
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₇ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₇×#2195

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₇	#447
commutator, Frattini, cosocle	C₂×C₈	C₂³×C₁₇
prime radical	C₁₇×#578	C₂
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₇ ◁ C₂×C₄×C₁₇ ◁ C₁₇×#131 ◁ G

206 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 206 conjugacy classes of subgroups — too many to draw. Only its 64 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) = 81
transitive degree	μ_t(G) = 1088

A minimal faithful permutation representation — 3 generators on 81 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19,25,31)(20,32,36,60)(21,37,40,57)(22,41,45,55)(23,30,24,29)(26,48,51,34)(27,46,53,39)(28,43,56,44)(33,61,65,78)(35,66,47,54)(38,69,72,52)(42,58,73,50)(49,70,77,81)(59,64,80,63)(62,67,75,76)(68,74,79,71);(18,20)(19,26)(21,33)(22,42)(23,35)(24,47)(25,36)(27,49)(28,54)(29,50)(30,58)(31,51)(32,41)(34,44)(37,67)(38,70)(39,63)(40,65)(43,48)(45,73)(46,64)(52,78)(53,77)(55,60)(56,66)(57,76)(59,68)(61,69)(62,71)(72,81)(74,75)(79,80);(18,21,25,40)(19,27,31,53)(20,33,36,65)(22,38,45,72)(23,46,24,39)(26,49,51,77)(28,52,56,69)(29,57,30,37)(32,59,60,80)(34,62,48,75)(35,64,47,63)(41,68,55,79)(42,70,73,81)(43,74,44,71)(50,76,58,67)(54,78,66,61)

Conjugacy classes & character table

391 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	D₁₇×#2195, #17188283, #17188300, …
maximal subgroup of	C₂×C₁₇×#2195, C₁₇×#33538, C₁₇×#33540, …
maximal normal subgroup of	C₂×C₁₇×#2195, C₁₇×#33538, C₁₇×#33540, …
maximal quotient of	C₁₇×#12112, C₁₇×#12113, C₁₇×#12168, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 927);