C₂×C₁₇×#360 #14525150

order	2176
nilpotency class	4
isoclinism	isoclinic class of #360
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₇ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₂×C₁₇×#360

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₇	#102
commutator	C₈	C₂²×C₄×C₁₇
Frattini, cosocle	C₂×C₈	C₂³×C₁₇
prime radical	C₂×C₁₇×#135	C₂
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₂²×C₄×C₁₇ ◁ C₂²×C₈×C₁₇ ◁ G

232 conjugacy classes of subgroups; only the 104 normal subgroups are shown.

normal subgroups only

This group has 232 conjugacy classes of subgroups — too many to draw. Only its 104 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 — 3 generators on 35 points:

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

Conjugacy classes & character table

544 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#360×Dic₁₇, #16949620, #16949981, …
maximal subgroup of	C₄×C₁₇×#360, C₁₇×#12650, C₁₇×#12735, …
maximal normal subgroup of	C₄×C₁₇×#360, C₁₇×#12650, C₁₇×#12735, …
maximal quotient of	C₂×C₁₇×#1333, C₂×C₁₇×#1334, C₁₇×#11598, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 876);