C₁₇×#2214 #14525220

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

Aliases

direct product

C₁₇×#2214

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₇	#459
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

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

normal subgroups only

This group has 150 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)(18,19,25,31)(20,29,34,40)(21,35,37,48)(22,30,24,28)(23,26,33,41)(27,42,44,32)(36,49,39,45)(38,46,47,43);(18,20,24,33,25,34,22,23)(19,26,30,40,31,41,28,29)(21,32,39,47,37,42,36,38)(27,35,46,49,44,48,43,45);(18,21)(19,27)(20,32)(22,36)(23,38)(24,39)(25,37)(26,35)(28,43)(29,45)(30,46)(31,44)(33,47)(34,42)(40,49)(41,48)

Conjugacy classes & character table

391 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#16947726, #16947731, #16947741, …
maximal subgroup of	C₁₇×#12312, C₁₇×#12313, C₁₇×#12315, …
maximal normal subgroup of	C₁₇×#12312, C₁₇×#12313, C₁₇×#12315, …
maximal quotient of	C₁₇×#12422, C₁₇×#12423, C₁₇×#12426, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 946);