C₁₇×#2375 #14525381

order	2176
nilpotency class	2
isoclinism	isoclinic class of #560
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄×C₁₇ · Schur multiplier (H₂) = C₂²×C₄²

Aliases

direct product

C₁₇×#2375

Subgroups

	subgroup	G/H
center, socle	C₂³×C₁₇	C₂⁴
commutator	C₂²	C₂³×C₄×C₁₇
Frattini, cosocle	C₂³	C₂⁴×C₁₇
prime radical	C₂×C₁₇×#120	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₇ ◁ G

688 conjugacy classes of subgroups; only the 264 normal subgroups are shown.

normal subgroups only

This group has 688 conjugacy classes of subgroups — too many to draw. Only its 264 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) = 544

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

Conjugacy classes & character table

646 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#16951091, #16951598, D₁₇×#2375, …
maximal subgroup of	C₁₇×#12960, C₁₇×#13043, C₂×C₁₇×#2375, …
maximal normal subgroup of	C₁₇×#12960, C₁₇×#13043, C₂×C₁₇×#2375, …
maximal quotient of	C₁₇×#13827, C₁₇×#13831, C₁₇×#13832, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 1107);