C₁₇×#2987 #14525993

order	2176
nilpotency class	2
isoclinism	isoclinic class of #560
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄×C₁₇ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₁₇×#2987

Subgroups

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

314 conjugacy classes of subgroups; only the 248 normal subgroups are shown.

normal subgroups only

This group has 314 conjugacy classes of subgroups — too many to draw. Only its 248 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 — 4 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)(21,24)(22,25)(23,28)(27,32)(29,31)(30,33)(34,35,37,41,38,40,44,47)(36,39,43,46,42,45,48,49);(18,20,22,28)(19,23,25,26)(21,29,30,27)(24,32,33,31)(34,36)(35,39)(37,43)(38,42)(40,45)(41,46)(44,48)(47,49);(18,21,22,30)(19,24,25,33)(20,27,28,29)(23,31,26,32)(35,40)(36,42)(41,47)(43,48);(19,25)(23,26)(24,33)(31,32)(36,42)(39,45)(43,48)(46,49)

Conjugacy classes & character table

646 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#16928732, #16929278, #16929288, …
maximal subgroup of	C₁₇×#8919, C₁₇×#9006, C₁₇×#9008, …
maximal normal subgroup of	C₁₇×#8919, C₁₇×#9006, C₁₇×#9008, …
maximal quotient of	C₁₇×#20539, C₁₇×#20542, C₁₇×#20576, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 1719);