C₁₇×#2218 #14525224

order	2176
nilpotency class	4
isoclinism	isoclinic class of #2218
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₇ · Schur multiplier (H₂) = C₂×C₄

Aliases

direct product

C₁₇×#2218

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₇	C₂×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂³×C₁₇
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₂²×C₄×C₁₇ ◁ C₂²×C₈×C₁₇ ◁ G

170 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 170 conjugacy classes of subgroups — too many to draw. Only its 64 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 — 3 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)(23,27)(24,28)(25,31)(29,33)(30,37)(32,36)(34,35);(22,23,28,35,25,30,32,33,26,29,36,37,31,34,24,27);(19,21)(23,29)(27,33)(30,34)(35,37)

Conjugacy classes & character table

442 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#16921891, #16921897, #16954996, …
maximal subgroup of	C₁₇×#7422, C₁₇×#7424, C₁₇×#13667, …
maximal normal subgroup of	C₁₇×#7422, C₁₇×#7424, C₁₇×#13667, …
maximal quotient of	C₁₇×#12433, C₁₇×#12442, C₁₇×#12454, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 950);