C₁₇×#11572 #16869316

order	4352
nilpotency class	4
isoclinism	isoclinic class of #11549
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₇ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₇×#11572

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₇	C₂×#99
commutator	C₂²×C₄	C₂²×C₄×C₁₇
Frattini, cosocle	C₂×C₄⋊C₄	C₂³×C₁₇
prime radical	C₂²×D₄×C₁₇	C₂×C₄
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₂²×C₄×C₁₇ ◁ C₂×C₄×D₄×C₁₇ ◁ G

416 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 102 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) = 49
transitive degree	μ_t(G) = 1088

A minimal faithful permutation representation — 3 generators on 49 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19,22,26,23,27,21,25)(20,24,28,31,29,32,30,33)(34,35)(36,42,43,48)(37,45,46,40)(38,41)(39,44)(47,49);(18,20)(19,24)(21,30)(22,28)(23,29)(25,33)(26,31)(27,32)(34,36)(35,39,41,47)(37,44)(38,43)(40,42,45,48)(46,49);(18,21,23,22)(19,25,27,26)(20,28,29,30)(24,31,32,33)(36,43)(39,47)(42,48)(44,49)

Conjugacy classes & character table

629 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 4560);