C₁₇×#2979 #14525985

order	2176
nilpotency class	2
isoclinism	isoclinic class of D₄²
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄×C₁₇ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₁₇×#2979

Subgroups

	subgroup	G/H
center	C₂×C₄×C₁₇	C₂⁴
commutator	C₂²	C₂³×C₄×C₁₇
Frattini, cosocle	C₂×C₄	C₂⁴×C₁₇
socle	C₂²×C₁₇	C₂³×C₄
prime radical	C₁₇×#532	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₇ ◁ G

410 conjugacy classes of subgroups; only the 256 normal subgroups are shown.

normal subgroups only

This group has 410 conjugacy classes of subgroups — too many to draw. Only its 256 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)(18,19)(20,24)(21,23)(22,25)(26,27,29,32,30,33,36,39)(28,31,35,38,34,37,40,41);(18,20)(19,22)(21,25)(23,24)(26,28)(27,31)(29,35)(30,34)(32,38)(33,37)(36,40)(39,41);(20,25)(22,24)(26,28)(27,31)(29,35)(30,34)(32,38)(33,37)(36,40)(39,41);(19,23)(22,24)(28,34)(31,37)(35,40)(38,41)

Conjugacy classes & character table

850 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#16928827, #16928832, #16929635, …
maximal subgroup of	C₁₇×#8934, C₁₇×#8935, C₁₇×#9067, …
maximal normal subgroup of	C₁₇×#8934, C₁₇×#8935, C₁₇×#9067, …
maximal quotient of	C₁₇×#20530, C₁₇×#20538, C₁₇×#20562, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 1711);