C₁₇×#7380 #16865124

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

Aliases

direct product

C₁₇×#7380

Subgroups

	subgroup	G/H
center	C₂×C₈×C₁₇	C₂²⋊C₄
commutator	C₂×C₄	C₂×C₁₆×C₁₇
Frattini, cosocle	C₄×C₁₆	C₂²×C₁₇
socle	C₂²×C₁₇	C₂²⋊C₁₆
prime radical	C₂×D₄×C₁₇	C₁₆
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₈×C₁₇ ◁ C₄×C₁₆×C₁₇ ◁ G

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

normal subgroups only

This group has 128 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) = 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)(20,22)(21,24)(23,25)(26,27,28,33,30,34,37,45,31,35,38,46,41,47,50,55,29,32,36,42,39,43,48,52,40,44,49,53,51,54,56,57);(19,22)(20,25)(23,24)(27,32)(28,36)(34,43)(35,44)(37,48)(38,49)(47,54)(50,56)

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, 368);