C₁₇×#2736 #14525742

order	2176
nilpotency class	2
isoclinism	isoclinic class of #2668
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₇ · Schur multiplier (H₂) = C₂×C₄²

Aliases

direct product

C₁₇×#2736

Subgroups

	subgroup	G/H
center, socle	C₂³×C₁₇	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁴×C₁₇
prime radical	C₂⁵×C₁₇	C₂²
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₇ ◁ G

560 conjugacy classes of subgroups; only the 176 normal subgroups are shown.

normal subgroups only

This group has 560 conjugacy classes of subgroups — too many to draw. Only its 176 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) = 544

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

Conjugacy classes & character table

544 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#16946944, #16947428, #17241436, …
maximal subgroup of	C₁₇×#12188, C₁₇×#12264, C₁₇×#36725, …
maximal normal subgroup of	C₁₇×#12188, C₁₇×#12264, C₁₇×#36725, …
maximal quotient of	C₁₇×#14366, C₁₇×#14481, C₁₇×#14577, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 1468);