C₁₇×#2213 #14525219

order	2176
nilpotency class	4
isoclinism	isoclinic class of #2212
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₇ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₇×#2213

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₇	#459
commutator, Frattini, cosocle	C₂×C₈	C₂³×C₁₇
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₇ ◁ C₂×C₄×C₁₇ ◁ C₄×C₈×C₁₇ ◁ G

170 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 170 conjugacy classes of subgroups — too many to draw. Only its 60 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)(19,22)(20,25)(21,23)(26,27)(28,33)(29,32)(30,31);(18,19,23,26,24,27,21,22)(20,25,31,33,29,32,28,30);(18,20)(19,25)(21,28)(22,30)(23,31)(24,29)(26,33)(27,32)

Conjugacy classes & character table

391 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#16947716, #16947721, #16947736, …
maximal subgroup of	C₁₇×#12310, C₁₇×#12311, C₁₇×#12314, …
maximal normal subgroup of	C₁₇×#12310, C₁₇×#12311, C₁₇×#12314, …
maximal quotient of	C₁₇×#12418, C₁₇×#12419, C₁₇×#12424, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 945);