C₁₇×#3531 #14526537

order	2176
nilpotency class	2
isoclinism	isoclinic class of #560
automorphism	?
homology	Abelianization (H₁) = C₂⁵×C₁₇ · Schur multiplier (H₂) = C₂⁸

Aliases

direct product

C₁₇×#3531

Subgroups

	subgroup	G/H
center	C₂×C₄×C₁₇	C₂⁴
commutator, Frattini, cosocle	C₂²	C₂⁵×C₁₇
socle	C₂²×C₁₇	C₂⁵
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₇ ◁ G

930 conjugacy classes of subgroups; only the 760 normal subgroups are shown.

normal subgroups only

This group has 930 conjugacy classes of subgroups — too many to draw. Only its 760 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 — 5 generators on 49 points:

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

Conjugacy classes & character table

646 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#16926762, #17015522, #17015534, …
maximal subgroup of	C₁₇×#8505, C₁₇×#18990, C₁₇×#18991, …
maximal normal subgroup of	C₁₇×#8505, C₁₇×#18990, C₁₇×#18991, …
maximal quotient of	C₁₇×#34348, C₁₇×#34350, C₄×C₁₇×#562, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 2263);