C₁₇×#12704 #16870448

order	4352
nilpotency class	4
isoclinism	isoclinic class of #11508
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₇ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₁₇×#12704

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₇	C₂×#99
commutator	C₂²×C₄	C₂²×C₄×C₁₇
Frattini, cosocle	C₂²×Q₈	C₂³×C₁₇
prime radical	C₂²×#41×C₁₇	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₂²×C₄×C₁₇ ◁ C₂²×#41×C₁₇ ◁ G

962 conjugacy classes of subgroups; only the 150 normal subgroups are shown.

normal subgroups only

This group has 962 conjugacy classes of subgroups — too many to draw. Only its 150 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) = 53
transitive degree	μ_t(G) = 1088

A minimal faithful permutation representation — 3 generators on 53 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19)(20,21)(22,23,27,32,28,33,25,30)(24,34,37,52,38,49,35,51)(26,40,39,50,42,31,43,48)(29,44,45,41,46,53,47,36);(22,24,28,38)(23,29,33,46)(25,37,27,35)(26,41,42,36)(30,47,32,45)(31,49,40,34)(39,44,43,53)(48,51,50,52);(19,21)(22,25,28,27)(23,30,33,32)(24,35,38,37)(26,39,42,43)(29,45,46,47)(31,48,40,50)(34,51,49,52)(36,44,41,53)

Conjugacy classes & character table

578 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 5692);