C₁₇×#1831 #14524837

order	2176
nilpotency class	2
isoclinism	isoclinic class of #120
automorphism	?
homology	Abelianization (H₁) = C₂²×C₈×C₁₇ · Schur multiplier (H₂) = C₂²×C₄

Aliases

direct product

C₁₇×#1831

Subgroups

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

260 conjugacy classes of subgroups; only the 160 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 160 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) = 37
transitive degree	μ_t(G) = 2176

A minimal faithful permutation representation — 3 generators on 37 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(19,20)(22,23)(24,27)(25,26)(28,29)(30,31,32,34,33,35,36,37);(18,19,21,20)(23,26)(27,29);(18,20,21,19)(22,24,25,28)(23,27,26,29)

Conjugacy classes & character table

952 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#16920857, #16920866, #16920888, …
maximal subgroup of	C₁₇×#7018, C₁₇×#7022, C₁₇×#7030, …
maximal normal subgroup of	C₁₇×#7018, C₁₇×#7022, C₁₇×#7030, …
maximal quotient of	C₁₇×#8780, C₁₇×#8781, C₁₇×#8784, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 563);