C₁₇×#12778 #16870522

order	4352
nilpotency class	4
isoclinism	isoclinic class of #12778
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₇ · Schur multiplier (H₂) = C₂⁴×C₄

Aliases

direct product

C₁₇×#12778

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₇	#1790
commutator	C₂×Q₈	C₂²×C₄×C₁₇
Frattini, cosocle	C₂×#41	C₂³×C₁₇
prime radical	C₁₇×#3549	C₂
LCS	G ▷ C₂×Q₈ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₇ ◁ C₂×C₄×C₁₇ ◁ C₂×#41×C₁₇ ◁ G

860 conjugacy classes of subgroups; only the 138 normal subgroups are shown.

normal subgroups only

This group has 860 conjugacy classes of subgroups — too many to draw. Only its 138 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)(20,28,30,32)(21,25,31,24)(22,26)(23,27)(29,33);(19,24)(21,31)(22,29)(25,27)(26,28)(32,33);(18,20)(19,24)(21,29)(22,31)(23,30)(25,27)(26,32)(28,33)

Conjugacy classes & character table

578 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 5766);