C₁₇×#2235 #14525241

order	2176
nilpotency class	4
isoclinism	isoclinic class of #2184
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₇ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₁₇×#2235

Subgroups

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

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

normal subgroups only

This group has 140 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) = 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)(26,27,30,34)(28,31,37,40)(29,38,36,33)(32,41,39,35);(19,22)(23,25);(18,20,21,24)(19,23,22,25)(27,31)(28,35)(29,36)(32,33)(34,40)(37,41)(38,39)

Conjugacy classes & character table

493 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#16947528, #16947535, #16947566, …
maximal subgroup of	C₁₇×#12279, C₁₇×#12280, C₁₇×#12285, …
maximal normal subgroup of	C₁₇×#12279, C₁₇×#12280, C₁₇×#12285, …
maximal quotient of	C₁₇×#12866, C₁₇×#12920, C₁₇×#12993, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 967);