C₁₇×#7362 #16865106

order	4352
nilpotency class	3
isoclinism	isoclinic class of #99
automorphism	?
homology	Abelianization (H₁) = C₂×C₁₇×C₃₂ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₇×#7362

Subgroups

	subgroup	G/H
center	C₂×C₈×C₁₇	C₂²⋊C₄
commutator	C₂²	C₂×C₁₇×C₃₂
Frattini, cosocle	C₂²×C₁₆	C₂²×C₁₇
socle	C₂²×C₁₇	C₂²⋊C₁₆
prime radical	C₂³×C₁₇	C₂×C₁₆
LCS	G ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₈×C₁₇ ◁ C₂²×C₁₆×C₁₇ ◁ G

138 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 138 conjugacy classes of subgroups — too many to draw. Only its 66 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 — 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)(26,27,28,32,29,33,36,42,30,34,37,43,39,45,48,52,31,35,38,44,40,46,49,53,41,47,50,54,51,55,56,57);(18,20,21,25)(19,22,23,24)

Conjugacy classes & character table

1496 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 350);