C₂×#34064205 #50310450

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

Aliases

direct product

C₂×#34064205

Splittings

Fitting, socle	C₂×C₁₃²×C₁₉ ⋊ C₂×C₃
derived, Hall	C₁₃²×C₁₉ ⋊ C₂²×C₃
Hall	C₂×C₁₃⋊D₂₄₇ ⋊ C₃
Hall	#23751431 ⋊ C₂²
Sylow	C₁₃² ⋊ C₂×D₁₉⋊C₃
Sylow	C₁₉ ⋊ C₂×#11759815

Subgroups

	subgroup	G/H
center, hypercenter	C₂	#34064205
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:

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

Conjugacy classes & character table

1082 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(38532, 332);

C2×#34064205 #50310450