C₁₇×#1688 #14524694

order	2176
nilpotency class	3
isoclinism	isoclinic class of #1685
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₇ · Schur multiplier (H₂) = C₄

Aliases

direct product

C₁₇×#1688

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₇	#121
commutator, Frattini, cosocle	C₄²	C₂³×C₁₇
prime radical	C₁₇×#493	C₂
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₄²×C₁₇ ◁ G

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

normal subgroups only

This group has 184 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) = 33
transitive degree	μ_t(G) = 1088

A minimal faithful permutation representation — 3 generators on 33 points:

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

Conjugacy classes & character table

391 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#16947886, #16947893, #16948054, …
maximal subgroup of	C₁₇×#12336, C₁₇×#12337, C₁₇×#12360, …
maximal normal subgroup of	C₁₇×#12336, C₁₇×#12337, C₁₇×#12360, …
maximal quotient of	C₁₇×#8653, C₁₇×#9230, C₁₇×#9572, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 420);