C₅×#3549⋊C₃ #14511398

order	1920
isoclinism	isoclinic class of #3549⋊C₃
automorphism	?
homology	Abelianization (H₁) = C₂×C₃×C₅ · Schur multiplier (H₂) = C₂³×C₄

Aliases

direct product	C₅×#3549⋊C₃
unambiguous semidirect product	#3549⋊(C₃×C₅)
unambiguous semidirect product	(C₅×#3549)⋊C₃

Splittings

Fitting, Hall	C₅×#3549 ⋊ C₃
derived	H(3,𝔽₄) ⋊ C₂×C₃×C₅
Sylow	#3549 ⋊ C₃×C₅

Subgroups

	subgroup	G/H
center, hypercenter	C₅	#3549⋊C₃
commutator, cosocle, hypocenter	H(3,𝔽₄)	C₂×C₃×C₅
Frattini	C₂²	C₂×C₅×C₂²⋊A₄
Fitting	C₅×#3549	C₃
socle	C₂²×C₅	C₂×C₂²⋊A₄
LCS	G ▷ H(3,𝔽₄)
UCS	C₁ ◁ C₅

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

normal subgroups only

This group has 486 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)(6,7,21,11,12,13)(8,27,24)(9,19,25,10,15,28)(14,26,20)(16,17,23)(18,22,29);(6,10,11,9)(7,19,12,15)(8,20,16,18)(14,17,22,27)(23,24)(26,29);(6,18,11,20)(7,17,12,27)(8,10,16,9)(13,25)(14,15,22,19)(21,28)(23,29)(24,26)

Conjugacy classes & character table

90 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 237096);