C₁₇×#2399 #14525405

order	2176
nilpotency class	2
isoclinism	isoclinic class of #392
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₇ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₁₇×#2399

Subgroups

	subgroup	G/H
center	C₂²×C₄×C₁₇	C₂³
commutator, Frattini, cosocle	C₂³	C₂⁴×C₁₇
socle, prime radical	C₂³×C₁₇	C₂⁴
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₇ ◁ G

504 conjugacy classes of subgroups; only the 248 normal subgroups are shown.

normal subgroups only

This group has 504 conjugacy classes of subgroups — too many to draw. Only its 248 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)(22,23,26,29)(24,28,25,27)(30,31,34,37)(32,36,33,35);(18,19)(20,21)(22,24,26,25)(23,27,29,28)(30,32,34,33)(31,35,37,36);(19,21)(22,24,26,25)(23,28,29,27)(30,33,34,32)(31,36,37,35);(22,25,26,24)(23,27,29,28)

Conjugacy classes & character table

748 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#16929399, #16935177, #16935194, …
maximal subgroup of	C₁₇×#9030, C₁₇×#10014, C₁₇×#10017, …
maximal normal subgroup of	C₁₇×#9030, C₁₇×#10014, C₁₇×#10017, …
maximal quotient of	C₁₇×#13848, C₁₇×#13850, C₁₇×#13856, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 1131);