C₁₇×#11496 #16869240

order	4352
nilpotency class	3
isoclinism	isoclinic class of #327
automorphism	?
homology	Abelianization (H₁) = C₂²×C₈×C₁₇ · Schur multiplier (H₂) = C₂×C₄

Aliases

direct product

C₁₇×#11496

Subgroups

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

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

normal subgroups only

This group has 296 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) = 65
transitive degree	μ_t(G) = 2176

A minimal faithful permutation representation — 3 generators on 65 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19)(20,26,28,23)(21,24)(22,25)(27,32,33,30)(29,31)(34,35,39,45,41,44,53,61,40,46,52,62,38,54,37,43)(36,47,50,57,49,42,56,58,51,60,64,65,55,59,48,63);(18,20,22,28)(19,23,25,26)(21,27,29,33)(24,30,31,32)(34,36,40,51)(35,42,46,59)(37,48,53,56)(38,55,41,49)(39,50,52,64)(43,57,61,65)(44,60,54,47)(45,58,62,63);(18,21,22,29)(19,24,25,31)(20,27,28,33)(23,30,26,32)(34,37,38,52,40,53,41,39)(35,43,54,62,46,61,44,45)(36,48,55,64,51,56,49,50)(42,57,47,63,59,65,60,58)

Conjugacy classes & character table

1292 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 4484);