C₁₇×#2571 #14525577

order	2176
nilpotency class	2
isoclinism	isoclinic class of #2403
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₇ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₁₇×#2571

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

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

normal subgroups only

This group has 380 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)(18,19,22,20)(21,24,25,23)(27,29)(31,32)(34,35,38,41)(36,40,37,39);(19,20)(23,24)(26,27,30,29)(28,31,33,32)(34,36,38,37)(35,39,41,40);(18,20,22,19)(21,24,25,23)(26,28,30,33)(27,31,29,32)(34,35)(36,39)(37,40)(38,41);(18,21,22,25)(19,23,20,24)(26,29,30,27)(28,32,33,31)(34,37,38,36)(35,40,41,39)

Conjugacy classes & character table

646 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#16937348, #16937353, #16937358, …
maximal subgroup of	C₁₇×#10351, C₁₇×#10352, C₁₇×#10353, …
maximal normal subgroup of	C₁₇×#10351, C₁₇×#10352, C₁₇×#10353, …
maximal quotient of	C₁₇×#13911, C₁₇×#13982, C₁₇×#14030, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 1303);