C₁₇×#11837 #16869581

order	4352
nilpotency class	4
isoclinism	isoclinic class of #11836
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₇ · Schur multiplier (H₂) = C₂×C₄

Aliases

direct product

C₁₇×#11837

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₇	#1514
commutator	C₂×C₈	C₂²×C₄×C₁₇
Frattini, cosocle	C₂×M₁₆	C₂³×C₁₇
prime radical	C₁₇×#3184	C₂
LCS	G ▷ C₂×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₇ ◁ C₂×C₄×C₁₇ ◁ C₄×M₁₆×C₁₇ ◁ G

324 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 90 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)(18,19)(20,28,30,23)(21,24)(22,27)(25,29,32,33)(26,31);(19,23)(20,29)(21,31)(24,32)(25,26)(27,28)(30,33);(19,24,27,26)(20,30)(23,32,28,25)(29,33)

Conjugacy classes & character table

476 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 4825);