C₁₇×#2310 #14525316

order	2176
nilpotency class	2
isoclinism	isoclinic class of #534
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄×C₁₇ · Schur multiplier (H₂) = C₂⁵×C₄

Aliases

direct product

C₁₇×#2310

Subgroups

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

784 conjugacy classes of subgroups; only the 360 normal subgroups are shown.

normal subgroups only

This group has 784 conjugacy classes of subgroups — too many to draw. Only its 360 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)(19,21)(22,23,24,25)(27,31)(28,34)(29,37)(39,41);(26,27,30,31)(28,35,34,32)(29,33,37,38)(36,41,40,39);(18,19)(20,21)(22,23)(24,25)(26,28,30,34)(27,32,31,35)(29,36,37,40)(33,39,38,41);(26,29)(27,33)(28,36)(30,37)(31,38)(32,39)(34,40)(35,41)

Conjugacy classes & character table

748 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#16927846, #16927849, #16932058, …
maximal subgroup of	C₁₇×#8753, C₁₇×#8754, C₁₇×#9462, …
maximal normal subgroup of	C₁₇×#8753, C₁₇×#8754, C₁₇×#9462, …
maximal quotient of	C₁₇×#13776, C₁₇×#13786, C₁₇×#13795, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 1042);