C₁₇×#2190 #14525196

order	2176
nilpotency class	4
isoclinism	isoclinic class of #2190
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₇ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₇×#2190

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₇	#447
commutator, Frattini, cosocle	C₂×C₈	C₂³×C₁₇
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₇ ◁ C₂×C₄×C₁₇ ◁ C₂×M₁₆×C₁₇ ◁ G

226 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 226 conjugacy classes of subgroups — too many to draw. Only its 64 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) = 272

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

Conjugacy classes & character table

340 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#16946487, #16946497, #16946504, …
maximal subgroup of	C₁₇×#12114, C₁₇×#12116, C₁₇×#12117, …
maximal normal subgroup of	C₁₇×#12114, C₁₇×#12116, C₁₇×#12117, …
maximal quotient of	C₁₇×#12102, C₁₇×#12103, C₁₇×#12104, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 922);