A₅×#92789 #44478359

order	30420
automorphism	?
homology	Abelianization (H₁) = C₃ · Schur multiplier (H₂) = C₂×C₁₃

Aliases

direct product

A₅×#92789

Splittings

Fitting, Sylow	C₁₃² ⋊ C₃×A₅
socle, derived	C₁₃²×A₅ ⋊ C₃

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, socle, hypocenter	C₁₃²×A₅	C₃
Fitting, cosocle	C₁₃²	C₃×A₅
LCS	G ▷ C₁₃²×A₅
UCS	C₁

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 31
transitive degree	μ_t(G) = 195

A minimal faithful permutation representation — 2 generators on 31 points:

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

Conjugacy classes & character table

295 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30420, 948);

A5×#92789 #44478359