C₁₇×#7393 #16865137

order	4352
nilpotency class	3
isoclinism	isoclinic class of #327
automorphism	?
homology	Abelianization (H₁) = C₂×C₁₆×C₁₇ · Schur multiplier (H₂) = C₁

Aliases

direct product

C₁₇×#7393

Subgroups

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

110 conjugacy classes of subgroups; only the 62 normal subgroups are shown.

normal subgroups only

This group has 110 conjugacy classes of subgroups — too many to draw. Only its 62 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) = 4352

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

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, 381);