C₁₇×#1389 #14524395

order	2176
nilpotency class	4
isoclinism	isoclinic class of #360
automorphism	?
homology	Abelianization (H₁) = C₄²×C₁₇ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₇×#1389

Subgroups

	subgroup	G/H
center	C₄×C₁₇	#102
commutator	C₈	C₄²×C₁₇
Frattini, cosocle	C₂²×C₈	C₂²×C₁₇
socle	C₂×C₁₇	#340
prime radical	C₂³×C₁₇	SD₁₆
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₁₇ ◁ C₂²×C₄×C₁₇ ◁ C₂²×C₈×C₁₇ ◁ G

128 conjugacy classes of subgroups; only the 76 normal subgroups are shown.

normal subgroups only

This group has 128 conjugacy classes of subgroups — too many to draw. Only its 76 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 — 2 generators on 49 points:

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

Conjugacy classes & character table

544 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	D₁₇×#1389, #16949588, #16949609, …
maximal subgroup of	C₂×C₁₇×#1389, C₁₇×#12646, C₁₇×#12649, …
maximal normal subgroup of	C₂×C₁₇×#1389, C₁₇×#12646, C₁₇×#12649, …
maximal quotient of	C₁₇×#7159, C₁₇×#7175, C₁₇×#7177, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 121);