C₁₇×#1287 #14524293

order	2176
nilpotency class	3
isoclinism	isoclinic class of #1284
automorphism	?
homology	Abelianization (H₁) = C₄²×C₁₇ · Schur multiplier (H₂) = C₄

Aliases

direct product

C₁₇×#1287

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₇	#95
commutator	C₂×C₄	C₄²×C₁₇
Frattini, cosocle	C₂×C₄²	C₂²×C₁₇
prime radical	C₂³×C₁₇	C₄⋊C₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₂×C₄²×C₁₇ ◁ G

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

normal subgroups only

This group has 126 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) = 49
transitive degree	μ_t(G) = 1088

A minimal faithful permutation representation — 2 generators on 49 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19,21,26,23,27,22,25)(20,28,29,24,31,32,30,33)(34,35)(36,42,44,48)(37,40)(38,41)(39,43,46,49)(45,47);(18,20,22,30,23,31,21,29)(19,24,26,32,27,33,25,28)(34,36)(35,39,41,46)(37,43)(38,44)(40,42,47,48)(45,49)

Conjugacy classes & character table

544 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	D₁₇×#1287, #16924134, #16924138, …
maximal subgroup of	C₂×C₁₇×#1287, C₁₇×#7964, C₁₇×#7965, …
maximal normal subgroup of	C₂×C₁₇×#1287, C₁₇×#7964, C₁₇×#7965, …
maximal quotient of	C₁₇×#7018, C₁₇×#7021, C₁₇×#7023, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 19);