C₁₇×#15142 #16872886

order	4352
nilpotency class	2
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₇ · Schur multiplier (H₂) = C₂⁶×C₄²

Aliases

direct product

C₁₇×#15142

Subgroups

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

4382 conjugacy classes of subgroups; only the 590 normal subgroups are shown.

normal subgroups only

This group has 4382 conjugacy classes of subgroups — too many to draw. Only its 590 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) = 33
transitive degree	μ_t(G) = 2176

A minimal faithful permutation representation — 4 generators on 33 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(19,21)(23,24)(27,28);(22,23,25,24)(31,33);(26,27,29,28)(30,31)(32,33);(18,19,20,21)(22,24,25,23)(26,28,29,27)

Conjugacy classes & character table

1088 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 8130);