C₁₇×#3147 #14526153

order	2176
nilpotency class	3
isoclinism	isoclinic class of #465
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₇ · Schur multiplier (H₂) = C₂⁴×C₄

Aliases

direct product

C₁₇×#3147

Subgroups

	subgroup	G/H
center	C₂×C₄×C₁₇	C₂×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₁₇
socle	C₂²×C₁₇	C₂²×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₇ ◁ C₂×C₄²×C₁₇ ◁ G

572 conjugacy classes of subgroups; only the 224 normal subgroups are shown.

normal subgroups only

This group has 572 conjugacy classes of subgroups — too many to draw. Only its 224 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) = 1088

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

Conjugacy classes & character table

748 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#16929646, #16933671, #16933688, …
maximal subgroup of	C₁₇×#9069, C₁₇×#9750, C₁₇×#9753, …
maximal normal subgroup of	C₁₇×#9069, C₁₇×#9750, C₁₇×#9753, …
maximal quotient of	C₁₇×#19596, C₁₇×#19600, C₁₇×#19603, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 1879);