A₅×#92788 #44478358

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

Aliases

direct product

A₅×#92788

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

336 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 31
transitive degree	μ_t(G) = 845

A minimal faithful permutation representation — 3 generators on 31 points:

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

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, 947);

A5×#92788 #44478358