C₁₇×#13712 #16871456

order	4352
nilpotency class	5
isoclinism	isoclinic class of #13661
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₇ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₇×#13712

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₇	C₂×D₁₆
commutator, Frattini, cosocle	C₂×C₁₆	C₂³×C₁₇
prime radical	C₁₇×#2215	C₂
LCS	G ▷ C₂×C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₂²×C₄×C₁₇ ◁ C₂²×C₈×C₁₇ ◁ C₂²×C₁₆×C₁₇ ◁ G

186 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 186 conjugacy classes of subgroups — too many to draw. Only its 74 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) = 2176

A minimal faithful permutation representation — 3 generators on 57 points:

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

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, 6700);