C₁₇×#1638 #14524644

order	2176
nilpotency class	3
isoclinism	isoclinic class of #1619
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₇ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₇×#1638

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₇	#120
commutator, Frattini, cosocle	C₄²	C₂³×C₁₇
prime radical	C₂×D₄×C₁₇	D₄
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₄²×C₁₇ ◁ G

194 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 194 conjugacy classes of subgroups — too many to draw. Only its 68 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) = 49
transitive degree	μ_t(G) = 1088

A minimal faithful permutation representation — 3 generators on 49 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19,23,26)(20,27,29,32)(21,25,22,30)(24,31,33,28)(34,35,39,43)(36,44,47,48)(37,42,38,41)(40,46,49,45);(18,20)(19,24)(21,28)(22,31)(23,29)(25,32)(26,33)(27,30)(34,36,39,47)(35,40,43,49)(37,46,38,45)(41,48,42,44);(18,21,23,22)(19,25,26,30)(20,28,29,31)(24,32,33,27)(35,41)(37,38)(40,48)(42,43)(44,49)(45,46)

Conjugacy classes & character table

442 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	D₁₇×#1638, #17010095, #17010348, …
maximal subgroup of	C₂×C₁₇×#1638, C₁₇×#18494, C₁₇×#18521, …
maximal normal subgroup of	C₂×C₁₇×#1638, C₁₇×#18494, C₁₇×#18521, …
maximal quotient of	C₁₇×#7765, C₁₇×#7767, C₁₇×#7773, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 370);