C₁₇×#2242 #14525248

order	2176
nilpotency class	4
isoclinism	isoclinic class of #2215
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₇ · Schur multiplier (H₂) = C₄

Aliases

direct product

C₁₇×#2242

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₇	C₂×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂³×C₁₇
prime radical	C₂×D₈×C₁₇	C₂²
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₄²×C₁₇ ◁ C₄×C₈×C₁₇ ◁ G

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

normal subgroups only

This group has 138 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) = 57
transitive degree	μ_t(G) = 1088

A minimal faithful permutation representation — 3 generators on 57 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19)(20,23)(21,22)(24,25)(26,27)(28,40)(29,34)(30,48)(31,51)(32,52)(33,39)(35,44)(36,41)(37,50)(38,49)(42,54)(43,53)(45,57)(46,56)(47,55);(19,22)(23,25)(26,28,41,46,32,43,50,47,33,44,31,42,49,45,30,29)(27,34,48,57,38,54,51,35,39,55,37,53,52,56,36,40);(18,20,21,24)(19,23,22,25)(26,29,30,45,49,42,31,44,33,47,50,43,32,46,41,28)(27,35,36,54,52,57,37,34,39,40,51,56,38,53,48,55)

Conjugacy classes & character table

646 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	D₁₇×#2242, #17189623, #17189655, …
maximal subgroup of	C₂×C₁₇×#2242, C₁₇×#33697, C₁₇×#33702, …
maximal normal subgroup of	C₂×C₁₇×#2242, C₁₇×#33697, C₁₇×#33702, …
maximal quotient of	C₁₇×#12889, C₁₇×#13147, C₁₇×#13148, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 974);