C₁₇×#2139 #14525145

order	2176
nilpotency class	4
isoclinism	isoclinic class of #509
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₇ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₇×#2139

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₇	C₂×D₈
commutator	C₈	C₂²×C₄×C₁₇
Frattini, cosocle	C₂×C₈	C₂³×C₁₇
prime radical	C₂×C₁₇×#135	C₂
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₂²×C₄×C₁₇ ◁ C₂²×C₈×C₁₇ ◁ G

232 conjugacy classes of subgroups; only the 104 normal subgroups are shown.

normal subgroups only

This group has 232 conjugacy classes of subgroups — too many to draw. Only its 104 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) = 1088

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)(18,19,20,21)(23,27)(24,30)(25,32)(28,35)(29,36)(31,34)(33,37);(22,23)(24,31)(25,34)(26,28)(27,30)(29,32)(33,36)(35,37);(23,28)(27,35)(29,34)(31,36)

Conjugacy classes & character table

544 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#16949618, #16949998, #16950049, …
maximal subgroup of	C₁₇×#12650, C₁₇×#12739, C₁₇×#12748, …
maximal normal subgroup of	C₁₇×#12650, C₁₇×#12739, C₁₇×#12748, …
maximal quotient of	C₁₇×#11592, C₁₇×#11648, C₁₇×#11660, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 871);