C₂×#34064231 #50310445

order	38532
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₂×#34064231

Splittings

Fitting, socle	C₂×C₁₃²×C₁₉ ⋊ C₂×C₃
derived, Hall	C₁₃²×C₁₉ ⋊ C₂²×C₃
Hall	C₂×C₁₃²×D₁₉ ⋊ C₃
Hall	#23751432 ⋊ C₂²
Sylow	C₁₃² ⋊ C₂×D₁₉⋊C₃
Hall	C₂×D₁₉ ⋊ #92788
Sylow	C₁₉ ⋊ C₂²×#92788

Subgroups

	subgroup	G/H
center, hypercenter	C₂	#34064231
commutator, cosocle, hypocenter	C₁₃²×C₁₉	C₂²×C₃
Frattini	C₁	G
Fitting, socle	C₂×C₁₃²×C₁₉	C₂×C₃
LCS	G ▷ C₁₃²×C₁₉
UCS	C₁ ◁ C₂

320 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 47
transitive degree	μ_t(G) = 6422

A minimal faithful permutation representation — 3 generators on 47 points:

(4,5,7)(6,9,12)(8,11,10)(13,15,14)(17,18,20)(19,22,25)(21,24,23)(26,28,27)(30,34,35,31,32,36)(33,42,39,37,38,44)(40,45,47,46,43,41);(1,2)(16,17,19,18,21,25,22,26,28,20,23,27,24)(29,30,33,39,45,42,46,32,36,41,47,35,34,40,38,43,44,37,31);(3,4,6,5,8,12,9,13,15,7,10,14,11)

Conjugacy classes & character table

1250 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(38532, 327);

C2×#34064231 #50310445