C₁₇×#11574 #16869318

order	4352
nilpotency class	4
isoclinism	isoclinic class of #11549
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₇ · Schur multiplier (H₂) = C₄²

Aliases

direct product

C₁₇×#11574

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	C₂³×C₁₇	C₂×C₂²⋊C₄
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₂²×C₄×C₁₇ ◁ C₂×C₄×Q₈×C₁₇ ◁ G

374 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 374 conjugacy classes of subgroups — too many to draw. Only its 106 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)(36,40)(37,41,45,39)(38,42)(43,48)(44,47,49,46);(18,20)(19,24)(21,30)(22,28)(23,29)(25,33)(26,31)(27,32)(35,39,42,41)(36,43)(40,47,48,46)(44,49);(18,21,23,22)(19,25,27,26)(20,28,29,30)(24,31,32,33)(34,36,38,43)(35,40,42,48)(37,44,45,49)(39,46,41,47)

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, 4562);