C₁₇×#2231 #14525237

order	2176
nilpotency class	4
isoclinism	isoclinic class of #2230
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₇ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₁₇×#2231

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₇	#476
commutator, Frattini, cosocle	C₂×C₈	C₂³×C₁₇
prime radical	C₁₇×#135	C₂²
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₇ ◁ C₂×C₄×C₁₇ ◁ C₄×C₈×C₁₇ ◁ G

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

normal subgroups only

This group has 120 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)(18,19,24,29)(20,30,33,28)(21,34)(22,38,31,27)(23,25,40,42)(26,43)(32,46)(35,48)(36,47)(37,41)(39,44)(45,49);(18,20,31,40,24,33,22,23)(19,25,38,28,29,42,27,30)(21,32,36,49,37,43,35,39)(26,41,45,47,46,34,44,48);(18,21)(19,26)(20,32)(22,35)(23,39)(24,37)(25,41)(27,44)(28,47)(29,46)(30,48)(31,36)(33,43)(34,42)(38,45)(40,49)

Conjugacy classes & character table

391 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#16948715, #16948720, #16948729, …
maximal subgroup of	C₁₇×#12463, C₁₇×#12464, C₁₇×#12465, …
maximal normal subgroup of	C₁₇×#12463, C₁₇×#12464, C₁₇×#12465, …
maximal quotient of	C₁₇×#12824, C₁₇×#12950, C₁₇×#13116, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 963);