C₁₇×#1533 #14524539

order	2176
nilpotency class	3
isoclinism	isoclinic class of #1510
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₇ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₇×#1533

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₇	C₂×C₂²⋊C₄
commutator	C₂×C₄	C₂²×C₄×C₁₇
Frattini, cosocle	C₄²	C₂³×C₁₇
prime radical	C₂²×D₄×C₁₇	C₄
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₂×C₄²×C₁₇ ◁ G

248 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 248 conjugacy classes of subgroups — too many to draw. Only its 88 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 — 3 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)(28,34,36,41)(29,33)(30,32)(31,35,39,37)(38,40);(19,22)(20,24)(26,28)(27,31)(29,37)(30,36)(32,39)(33,41)(34,40)(35,38);(27,32)(31,39)(33,40)(34,41)

Conjugacy classes & character table

442 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#16922052, #16922094, #16926841, …
maximal subgroup of	C₁₇×#7481, C₁₇×#7495, C₁₇×#8522, …
maximal normal subgroup of	C₁₇×#7481, C₁₇×#7495, C₁₇×#8522, …
maximal quotient of	C₁₇×#7592, C₁₇×#7595, C₁₇×#7601, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 265);