D₅×#15690148 #44477682

order	30420
automorphism	?
homology	Abelianization (H₁) = C₂²×C₉ · Schur multiplier (H₂) = C₂

Aliases

direct product

D₅×#15690148

Splittings

derived, Hall	C₅×C₁₃² ⋊ C₂²×C₉
Hall	C₅×#13095200 ⋊ C₂²
Hall	D₅×C₁₃⋊D₁₃ ⋊ C₉
Hall	#13095200 ⋊ C₂×D₅
Sylow	C₁₃² ⋊ C₂×C₉×D₅
Sylow	C₅ ⋊ C₂×#15690148

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₃	D₅×#11759815
commutator, hypocenter	C₅×C₁₃²	C₂²×C₉
Fitting, socle, cosocle	C₃×C₅×C₁₃²	C₂²×C₃
prime radical	C₃×D₅×C₁₃⋊D₁₃	C₃
LCS	G ▷ C₅×C₁₃²
UCS	C₁ ◁ C₃

480 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 40
transitive degree	μ_t(G) = 7605

A minimal faithful permutation representation — 3 generators on 40 points:

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

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30420, 271);

D5×#15690148 #44477682