C₅×#85558 #14511296

order	1920
isoclinism	isoclinic class of #85558
automorphism	?
homology	Abelianization (H₁) = C₂×C₅ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₅×#85558

Splittings

Fitting	C₅×H(3,𝔽₄) ⋊ D₃
derived	#5464 ⋊ C₂×C₅

Subgroups

	subgroup	G/H
center, hypercenter	C₅	#85558
commutator, cosocle, hypocenter	#5464	C₂×C₅
Frattini	C₂²	C₅×#1020
Fitting	C₅×H(3,𝔽₄)	D₃
socle	C₂²×C₅	#1020
LCS	G ▷ #5464
UCS	C₁ ◁ C₅

206 conjugacy classes of subgroups; only the 16 normal subgroups are shown.

normal subgroups only

This group has 206 conjugacy classes of subgroups — too many to draw. Only its 16 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) = 29
transitive degree	μ_t(G) = 120

A minimal faithful permutation representation — 2 generators on 29 points:

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

Conjugacy classes & character table

60 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 236994);