C₁₇×#2402 #14525408

order	2176
nilpotency class	2
isoclinism	isoclinic class of #392
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₇ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₇×#2402

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

400 conjugacy classes of subgroups; only the 216 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 216 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) = 2176

A minimal faithful permutation representation — 4 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)(28,31)(29,33)(30,32)(34,35,37,39)(36,38,40,41);(19,22)(23,25)(26,28,30,29)(27,31,32,33)(34,36)(35,38)(37,40)(39,41);(26,29,30,28)(27,31,32,33)(36,40)(38,41);(18,20,21,24)(19,23,22,25)

Conjugacy classes & character table

748 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#16937459, #16937464, #17042668, …
maximal subgroup of	C₁₇×#10372, C₁₇×#10373, C₁₇×#21676, …
maximal normal subgroup of	C₁₇×#10372, C₁₇×#10373, C₁₇×#21676, …
maximal quotient of	C₁₇×#13846, C₁₇×#13848, C₁₇×#13854, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 1134);