C₁₇×#11490 #16869234

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×#11490

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	C₁₇×#532	C₄
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₈×C₁₇ ◁ C₂×C₄×C₈×C₁₇ ◁ G

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

normal subgroups only

This group has 364 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) = 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)(26,27,31,37,33,36,45,53,32,38,44,54,30,46,29,35)(28,39,42,49,41,34,48,50,43,52,56,57,47,51,40,55);(19,22)(20,24)(26,28)(27,34)(29,40)(30,47)(31,42)(32,43)(33,41)(35,49)(36,52)(37,50)(38,51)(39,46)(44,56)(45,48)(53,57)(54,55);(26,29,30,44,32,45,33,31)(27,35,46,54,38,53,36,37)(28,40,47,56,43,48,41,42)(34,49,39,55,51,57,52,50)

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, 4478);