C₅×#87498 #14511432

order	1920
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₅ · Schur multiplier (H₂) = C₂⁶

solvable

Aliases

direct product

C₅×#87498

Splittings

Fitting

C₅×#585 ⋊ D₃

Subgroups

	subgroup	G/H
center, socle	C₂×C₅	C₂³×S₄
commutator, cosocle, hypocenter	SL(2,𝔽₃)	C₂⁴×C₅
Frattini	C₂	C₂³×C₅×S₄
Fitting	C₅×#585	D₃
hypercenter	C₅×#41	S₄
LCS	G ▷ SL(2,𝔽₃)
UCS	C₁ ◁ C₂×C₅ ◁ C₅×#41

1518 conjugacy classes of subgroups; only the 200 normal subgroups are shown.

normal subgroups only

This group has 1518 conjugacy classes of subgroups — too many to draw. Only its 200 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) = 37
transitive degree	μ_t(G) = 160

A minimal faithful permutation representation — 4 generators on 37 points:

(1,2,3,4,5)(6,30,20,16,21,33,11,17,22,8,9,32)(7,34,28,23,24,37,12,26,29,13,14,36)(10,18,19,31)(15,27,25,35);(7,12)(13,23)(14,24)(15,25)(26,34)(27,35)(28,29)(36,37);(6,7)(8,13)(9,14)(10,15)(11,12)(16,23)(17,26)(18,27)(19,25)(20,28)(21,24)(22,29)(30,34)(31,35)(32,36)(33,37);(8,16)(9,19)(10,21)(13,23)(14,25)(15,24)(17,18)(20,22)(26,27)(28,29)(30,31)(34,35)

Conjugacy classes & character table

215 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 237130);