Finite Group Databasebeta

← Prev (#80935) Next (#80937) →

D₃×#472 #80936

order	384
automorphism	?
homology	Abelianization (H₁) = C₂⁴ · Schur multiplier (H₂) = C₂⁵

Aliases

Splittings

Fitting	C₃×#472 ⋊ C₂
Sylow	C₃ ⋊ C₂×#472

Subgroups

	subgroup	G/H
center	C₂	D₃×#121
commutator, cosocle	C₂×C₃×C₄	C₂⁴
Frattini	C₂×C₄	C₂³×D₃
Fitting	C₃×#472	C₂
socle	C₂×C₃	C₂×#121
hypercenter	#472	D₃
hypocenter	C₃	C₂×#472
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ #472

488 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 19
transitive degree	μ_t(G) = 48

A minimal faithful permutation representation — 4 generators on 19 points:

(1,3)(2,8)(4,11)(5,12)(6,13)(7,10)(9,16)(14,15)(17,18,19);(1,2,7,14,5,9,4,6)(3,8,10,15,12,16,11,13);(2,6)(3,10)(4,7)(9,14)(11,12)(13,15);(18,19)

Conjugacy classes & character table

48 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	D₃×#2192, D₃×#2193, #10949167, …
maximal normal subgroup of	D₃×#2192, D₃×#2193, #10949167, …
maximal quotient of	D₃×#1667, D₃×#1675, D₃×#1677, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(384, 13512);