C₂³×C₁₇×H(5,𝔽₂) #16920842

order	4352
nilpotency class	2
isoclinism	isoclinic class of H(5,𝔽₂)
automorphism	?
homology	Abelianization (H₁) = C₂⁷×C₁₇ · Schur multiplier (H₂) = C₂²⁰

Aliases

direct product

C₂³×C₁₇×H(5,𝔽₂)

Subgroups

	subgroup	G/H
center, socle	C₂⁴×C₁₇	C₂⁴
commutator, Frattini, cosocle	C₂	C₂⁷×C₁₇
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₁₇ ◁ G

65726 conjugacy classes of subgroups; only the 58526 normal subgroups are shown.

normal subgroups only

This group has 65726 conjugacy classes of subgroups — too many to draw. Only its 58526 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) = 31
transitive degree	μ_t(G) = 1088

A minimal faithful permutation representation — 7 generators on 31 points:

(1,2)(15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31);(3,4);(5,6);(7,8)(9,13)(10,11)(12,14);(8,11)(12,13);(7,8)(9,12)(10,11)(13,14);(7,9)(8,12)(10,14)(11,13)

Conjugacy classes & character table

2312 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 56086);