C₁₇×#1604 #14524610

order	2176
nilpotency class	3
isoclinism	isoclinic class of #1595
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₇ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₇×#1604

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₇	#120
commutator, Frattini, cosocle	C₂²×C₄	C₂³×C₁₇
prime radical	C₁₇×#537	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₂²×C₄×C₁₇ ◁ G

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

normal subgroups only

This group has 282 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) = 544

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)(18,19,21,24)(20,22,25,23)(30,33);(19,22)(20,25)(23,24)(26,27)(28,30)(29,31)(32,33);(26,28,29,32)(27,30,31,33)

Conjugacy classes & character table

391 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#16946555, #16946565, #16946572, …
maximal subgroup of	C₁₇×#12126, C₁₇×#12128, C₁₇×#12129, …
maximal normal subgroup of	C₁₇×#12126, C₁₇×#12128, C₁₇×#12129, …
maximal quotient of	C₁₇×#7752, C₁₇×#7754, C₁₇×#7764, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 336);