C₅×#20262573 #44538230

order	31460
automorphism	?
homology	Abelianization (H₁) = C₄×C₅ · Schur multiplier (H₂) = C₁₁

Aliases

direct product

C₅×#20262573

Splittings

Fitting, socle, Hall	C₅×C₁₁²×C₁₃ ⋊ C₄
derived, Hall	C₁₁²×C₁₃ ⋊ C₄×C₅
Hall	C₅×C₁₁² ⋊ #261
Sylow	C₁₁² ⋊ C₅×#261
Hall	C₅×C₁₃ ⋊ #92150
Sylow	C₁₃ ⋊ C₅×#92150

Subgroups

	subgroup	G/H
center, hypercenter	C₅	#20262573
commutator, hypocenter	C₁₁²×C₁₃	C₄×C₅
Frattini	C₁	G
Fitting, socle	C₅×C₁₁²×C₁₃	C₄
prime radical	C₅×C₁₁⋊D₁₄₃	C₂
cosocle	C₁₁⋊D₁₄₃	C₂×C₅
LCS	G ▷ C₁₁²×C₁₃
UCS	C₁ ◁ C₅

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 40
transitive degree	μ_t(G) = 1430

A minimal faithful permutation representation — 2 generators on 40 points:

(1,2,3,4,5)(6,7)(8,11,12,10)(9,14,15,21)(13,18,19,16)(17,24,22,27)(20,25,26,23)(29,30,31,33)(32,35,36,37)(34,39,40,38);(6,8,13,20,24,14,21,27,26,19,12)(7,17,25,10,9,18,16,15,11,23,22)(28,29,32,37,39,30,34,40,33,38,35,36,31)

Conjugacy classes & character table

1985 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31460, 170);

C5×#20262573 #44538230