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D₃×#544 #86595

order	384
automorphism	?
homology	Abelianization (H₁) = C₂⁵ · Schur multiplier (H₂) = C₂⁸

Aliases

Splittings

Fitting	C₃×#544 ⋊ C₂
Sylow	C₃ ⋊ C₂×#544

Subgroups

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₃
commutator, socle, cosocle	C₂²×C₃	C₂⁵
Fitting	C₃×#544	C₂
prime radical	C₂³×D₃	C₂³
hypercenter	#544	D₃
hypocenter	C₃	C₂×#544
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂² ◁ #544

1080 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 19
transitive degree	μ_t(G) = 96

A minimal faithful permutation representation — 5 generators on 19 points:

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

Conjugacy classes & character table

66 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	D₃×#1599, D₃×#1605, D₃×#1611, …
maximal normal subgroup of	D₃×#1599, D₃×#1605, D₃×#1611, …
maximal quotient of	D₃×#2316, D₃×#2317, D₃×#2329, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(384, 19171);