C₂×C₁₇×#560 #14526531

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

Aliases

direct product

C₂×C₁₇×#560

Subgroups

	subgroup	G/H
center, socle	C₂³×C₁₇	C₂⁴
commutator, Frattini, cosocle	C₂²	C₂⁵×C₁₇
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₇ ◁ G

1344 conjugacy classes of subgroups; only the 776 normal subgroups are shown.

normal subgroups only

This group has 1344 conjugacy classes of subgroups — too many to draw. Only its 776 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) = 35
transitive degree	μ_t(G) = 544

A minimal faithful permutation representation — 5 generators on 35 points:

(1,2)(19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35);(3,4)(5,12)(6,11)(7,9)(8,14)(10,16)(13,17)(15,18);(3,5)(4,8)(6,14)(7,15)(9,17)(10,18)(11,12)(13,16);(4,9)(5,13)(8,12)(10,11)(14,15)(17,18);(4,10)(5,14)(8,17)(9,11)(12,18)(13,15)

Conjugacy classes & character table

646 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#16950142, C₂×#14530791, #560×Dic₁₇, …
maximal subgroup of	C₁₇×#12762, C₂×C₁₇×#2200, C₄×C₁₇×#560, …
maximal normal subgroup of	C₁₇×#12762, C₂×C₁₇×#2200, C₄×C₁₇×#560, …
maximal quotient of	C₂×C₁₇×#2375, C₂×C₁₇×#2376, C₂×C₁₇×#2377, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 2257);