C₁₇×#2371 #14525377

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×#2371

Subgroups

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

448 conjugacy classes of subgroups; only the 280 normal subgroups are shown.

normal subgroups only

This group has 448 conjugacy classes of subgroups — too many to draw. Only its 280 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) = 37
transitive degree	μ_t(G) = 2176

A minimal faithful permutation representation — 4 generators on 37 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19,21,20)(23,26)(27,29)(30,31)(32,35)(33,34)(36,37);(18,20,21,19)(31,34)(35,37);(22,23)(24,27)(25,26)(28,29)(30,32,33,36)(31,35,34,37);(22,24,25,28)(23,27,26,29)(30,31)(32,35)(33,34)(36,37)

Conjugacy classes & character table

850 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#16931948, #16931958, D₁₇×#2371, …
maximal subgroup of	C₁₇×#9440, C₁₇×#9442, C₂×C₁₇×#2371, …
maximal normal subgroup of	C₁₇×#9440, C₁₇×#9442, C₂×C₁₇×#2371, …
maximal quotient of	C₁₇×#13805, C₁₇×#13815, C₁₇×#13825, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 1103);