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#41×C₃⋊D₃ #64365

order	288
automorphism	?
homology	Abelianization (H₁) = C₂⁴ · Schur multiplier (H₂) = C₂⁵×C₃

Aliases

#41×C₃⋊D₃

Splittings

Fitting	C₃²×#41 ⋊ C₂
Sylow	C₃² ⋊ C₂×#41

Subgroups

	subgroup	G/H
center	C₄	C₂²×C₃⋊D₃
commutator, socle, cosocle	C₂×C₃²	C₂⁴
Frattini	C₂	C₂³×C₃⋊D₃
Fitting	C₃²×#41	C₂
hypercenter	#41	C₃⋊D₃
hypocenter	C₃²	C₂×#41
LCS	G ▷ C₂×C₃² ▷ C₃²
UCS	C₁ ◁ C₄ ◁ #41

492 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 14
transitive degree	μ_t(G) = 72

A minimal faithful permutation representation — 4 generators on 14 points:

(10,11)(13,14);(1,3,4,7)(2,6,5,8)(12,13,14);(2,5)(6,8)(9,10,11);(1,2)(3,6)(4,5)(7,8)

Conjugacy classes & character table

60 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	#10591671, #10591672, C₃⋊D₃×#104, …
maximal normal subgroup of	#10591671, #10591672, C₃⋊D₃×#104, …
maximal quotient of	#10595988, C₃⋊D₃×#117, #10595993, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(288, 1013);