C₁₇×#9972 #16867716

order	4352
nilpotency class	3
isoclinism	isoclinic class of #9914
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₇ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₇×#9972

Subgroups

	subgroup	G/H
center, socle	C₂³×C₁₇	#120
commutator, Frattini, cosocle	C₂³×C₄	C₂³×C₁₇
prime radical	C₂⁴×C₁₇	C₂×D₄
LCS	G ▷ C₂³×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₇ ◁ C₂³×C₄×C₁₇ ◁ G

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

normal subgroups only

This group has 632 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) = 45
transitive degree	μ_t(G) = 1088

A minimal faithful permutation representation — 3 generators on 45 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19)(20,21)(22,23,26,24)(25,27,29,28)(30,31)(32,35)(33,36)(34,37)(38,41)(39,42)(40,44)(43,45);(23,27)(24,28)(25,29)(30,32,34,39)(31,35,37,42)(33,38,40,45)(36,43,44,41);(19,21)(22,24,26,23)(25,27,29,28)(30,33)(31,36)(32,38)(34,40)(35,41)(37,44)(39,45)(42,43)

Conjugacy classes & character table

680 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 2960);