C₁₇×#12110 #16869854

order	4352
nilpotency class	4
isoclinism	isoclinic class of #12108
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₇ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₇×#12110

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₇	#447
commutator, Frattini, cosocle	C₂²×C₈	C₂³×C₁₇
LCS	G ▷ C₂²×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₂²×C₄×C₁₇ ◁ C₁₇×#408 ◁ G

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

normal subgroups only

This group has 422 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) = 1088

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)(22,25)(26,27)(28,39)(29,33)(30,37)(31,36)(32,38)(34,41)(35,43)(40,53)(42,54)(44,51)(45,49)(46,50)(47,52)(48,57)(55,56);(18,19)(20,22)(21,23)(24,25)(27,33)(29,43)(30,31)(34,48)(35,37)(36,49)(38,50)(39,53)(40,56)(41,47)(44,57)(45,46)(51,54)(52,55);(18,20)(19,22)(21,24)(23,25)(26,28,32,42)(27,34,38,52)(29,44,46,40)(30,47,31,41)(33,48,50,55)(35,53,49,51)(36,54,37,39)(43,57,45,56)

Conjugacy classes & character table

527 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 5098);