C₅×#2030⋊C₃ #14510693

order	1920
isoclinism	isoclinic class of #2029⋊C₃
automorphism	?
homology	Abelianization (H₁) = C₂×C₃×C₅ · Schur multiplier (H₂) = C₂

solvable

Aliases

direct product	C₅×#2030⋊C₃
unambiguous semidirect product	#2030⋊(C₃×C₅)
unambiguous semidirect product	(C₅×#2030)⋊C₃

Splittings

Fitting, Hall	C₅×#2030 ⋊ C₃
Sylow	#2030 ⋊ C₃×C₅

Subgroups

	subgroup	G/H
center, socle, hypercenter	C₂²×C₅	#120⋊C₃
commutator, cosocle, hypocenter	#543	C₂×C₃×C₅
Frattini	C₂⁴	C₂×C₅×A₄
Fitting	C₅×#2030	C₃
prime radical	C₅×#543⋊C₃	C₂
LCS	G ▷ #543
UCS	C₁ ◁ C₂²×C₅

170 conjugacy classes of subgroups; only the 28 normal subgroups are shown.

normal subgroups only

This group has 170 conjugacy classes of subgroups — too many to draw. Only its 28 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) = 160

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

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

Conjugacy classes & character table

150 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 236391);