C₅×D₃×#11762245 #44570600

order	32490
automorphism	?
homology	Abelianization (H₁) = C₂×C₃×C₅ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₅×D₃×#11762245
unambiguous semidirect product	C₃⋊(C₂×C₅×#11762245)

Splittings

Fitting, socle	C₃×C₅×C₁₉² ⋊ C₂×C₃
derived	C₃×C₁₉² ⋊ C₂×C₃×C₅
Hall	C₃×C₅×#11762245 ⋊ C₂
Hall	C₃×#11762245 ⋊ C₂×C₅
Hall	C₅×C₁₉² ⋊ C₃×D₃
Sylow	C₁₉² ⋊ C₃×C₅×D₃

Subgroups

	subgroup	G/H
center, hypercenter	C₅	D₃×#11762245
commutator, cosocle, hypocenter	C₃×C₁₉²	C₂×C₃×C₅
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₁₉²	C₂×C₃
LCS	G ▷ C₃×C₁₉²
UCS	C₁ ◁ C₅

396 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 46
transitive degree	μ_t(G) = 5415

A minimal faithful permutation representation — 3 generators on 46 points:

(2,3)(4,5,6,7,8)(10,11,13)(12,15,16)(14,18,17)(19,23,21)(20,24,22)(25,27,26)(29,30,32)(31,34,35)(33,37,36)(38,42,40)(39,43,41)(44,46,45);(1,2,3)(28,29,31,35,40,45,42,30,33,38,43,32,36,41,34,39,44,46,37);(9,10,12,16,21,26,23,11,14,19,24,13,17,22,15,20,25,27,18)

Conjugacy classes & character table

1845 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32490, 184);

C5×D3×#11762245 #44570600