C₁₇×#2113 #14525119

order	2176
nilpotency class	2
isoclinism	isoclinic class of #120
automorphism	?
homology	Abelianization (H₁) = C₂²×C₈×C₁₇ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₇×#2113

Subgroups

	subgroup	G/H
center	C₂×C₈×C₁₇	C₂³
commutator	C₂²	C₂²×C₈×C₁₇
Frattini, cosocle	C₂×C₈	C₂³×C₁₇
socle	C₂²×C₁₇	C₂²×C₈
prime radical	C₂×#41×C₁₇	C₄
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₈×C₁₇ ◁ G

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

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 120 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) = 53
transitive degree	μ_t(G) = 1088

A minimal faithful permutation representation — 3 generators on 53 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19)(20,21)(22,23,25,29,26,30,35,41,27,31,36,42,37,43,47,51)(24,28,33,39,34,40,46,50,32,38,44,48,45,49,52,53);(19,21)(22,24)(23,28)(25,33)(26,34)(27,32)(29,39)(30,40)(31,38)(35,46)(36,44)(37,45)(41,50)(42,48)(43,49)(47,52)(51,53);(24,32)(28,38)(33,44)(34,45)(39,48)(40,49)(46,52)(50,53)

Conjugacy classes & character table

952 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#16921331, #16921334, #16921391, …
maximal subgroup of	C₁₇×#7207, C₁₇×#7208, C₁₇×#7227, …
maximal normal subgroup of	C₁₇×#7207, C₁₇×#7208, C₁₇×#7227, …
maximal quotient of	C₁₇×#11419, C₁₇×#11441, C₁₇×#11461, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 845);