C₁₇×#7418 #16865162

order	4352
nilpotency class	5
isoclinism	isoclinic class of #7418
automorphism	?
homology	Abelianization (H₁) = C₂×C₄×C₁₇ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₇×#7418

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₇	#357
commutator	C₂×C₁₆	C₂×C₄×C₁₇
Frattini, cosocle	C₂²×C₁₆	C₂²×C₁₇
prime radical	C₁₇×#2215	C₂
LCS	G ▷ C₂×C₁₆ ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₂²×C₄×C₁₇ ◁ C₂²×C₈×C₁₇ ◁ C₂²×C₁₆×C₁₇ ◁ G

162 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 162 conjugacy classes of subgroups — too many to draw. Only its 54 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) = 57
transitive degree	μ_t(G) = 1088

A minimal faithful permutation representation — 2 generators on 57 points:

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

Conjugacy classes & character table

833 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 406);