C₁₇×#2608 #14525614

order	2176
nilpotency class	2
isoclinism	isoclinic class of #2403
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₇ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₇×#2608

Subgroups

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

428 conjugacy classes of subgroups; only the 200 normal subgroups are shown.

normal subgroups only

This group has 428 conjugacy classes of subgroups — too many to draw. Only its 200 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) = 1088

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

Conjugacy classes & character table

646 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#16937563, #16937568, D₁₇×#2608, …
maximal subgroup of	C₁₇×#10388, C₁₇×#10389, C₂×C₁₇×#2608, …
maximal normal subgroup of	C₁₇×#10388, C₁₇×#10389, C₂×C₁₇×#2608, …
maximal quotient of	C₁₇×#13953, C₁₇×#14092, C₁₇×#14094, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 1340);