C₁₇×#2859 #14525865

order	2176
nilpotency class	2
isoclinism	isoclinic class of #2846
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₇ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₁₇×#2859

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂³×C₁₇	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁴×C₁₇
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₇ ◁ G

472 conjugacy classes of subgroups; only the 264 normal subgroups are shown.

normal subgroups only

This group has 472 conjugacy classes of subgroups — too many to draw. Only its 264 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) = 2176

A minimal faithful permutation representation — 4 generators on 37 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(19,21)(24,27)(25,29)(30,31,35,34)(32,37,36,33);(22,23,26,28)(24,25,27,29)(30,32)(31,33)(34,37)(35,36);(18,19,20,21)(22,24,26,27)(23,25,28,29)(30,33,35,37)(31,36,34,32);(22,25)(23,27)(24,28)(26,29)(30,34,35,31)(32,37,36,33)

Conjugacy classes & character table

748 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#16922684, #16922697, #16922776, …
maximal subgroup of	C₁₇×#7660, C₁₇×#7663, C₁₇×#7680, …
maximal normal subgroup of	C₁₇×#7660, C₁₇×#7663, C₁₇×#7680, …
maximal quotient of	C₁₇×#14687, C₁₇×#14699, C₁₇×#14707, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 1591);