C₅×#3444⋊C₃ #14511386

order	1920
isoclinism	isoclinic class of #3444⋊C₃
automorphism	?
homology	Abelianization (H₁) = C₂×C₃×C₅ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product	C₅×#3444⋊C₃
unambiguous semidirect product	#3444⋊(C₃×C₅)
unambiguous semidirect product	(C₅×#3444)⋊C₃

Splittings

Fitting, Hall	C₅×#3444 ⋊ C₃
derived	C₂²×C₄² ⋊ C₂×C₃×C₅
Sylow	#3444 ⋊ C₃×C₅

Subgroups

	subgroup	G/H
center, hypercenter	C₅	#3444⋊C₃
commutator, cosocle, hypocenter	C₂²×C₄²	C₂×C₃×C₅
Frattini	C₂²	C₂×C₅×C₂²⋊A₄
Fitting	C₅×#3444	C₃
socle	C₂²×C₅	C₂×C₂²⋊A₄
LCS	G ▷ C₂²×C₄²
UCS	C₁ ◁ C₅

464 conjugacy classes of subgroups; only the 34 normal subgroups are shown.

normal subgroups only

This group has 464 conjugacy classes of subgroups — too many to draw. Only its 34 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 — 3 generators on 29 points:

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

Conjugacy classes & character table

120 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 237084);