C₁₇×#2234 #14525240

order	2176
nilpotency class	4
isoclinism	isoclinic class of #2184
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₇ · Schur multiplier (H₂) = C₄

Aliases

direct product

C₁₇×#2234

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₇	C₂×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂³×C₁₇
prime radical	C₁₇×#466	C₂
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₂²×C₄×C₁₇ ◁ C₂²×C₈×C₁₇ ◁ G

142 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 142 conjugacy classes of subgroups — too many to draw. Only its 60 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) = 41
transitive degree	μ_t(G) = 1088

A minimal faithful permutation representation — 3 generators on 41 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)(27,31)(28,34)(30,37)(32,40)(33,36)(35,41)(38,39);(19,22)(23,25)(26,27,29,31)(28,32,35,39)(30,33,36,37)(34,38,41,40);(18,20,21,24)(19,23,22,25)(26,28,29,35)(27,32,31,39)(30,38,36,40)(33,41,37,34)

Conjugacy classes & character table

493 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	D₁₇×#2234, #17189122, #17189138, …
maximal subgroup of	C₂×C₁₇×#2234, C₁₇×#33645, C₁₇×#33647, …
maximal normal subgroup of	C₂×C₁₇×#2234, C₁₇×#33645, C₁₇×#33647, …
maximal quotient of	C₁₇×#12868, C₁₇×#12921, C₁₇×#12992, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 966);