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C₄×D₃₉ #64622

order	312
isoclinism	isoclinic class of D₃₉
automorphism	?
homology	Abelianization (H₁) = C₂×C₄ · Schur multiplier (H₂) = C₂

Aliases

C₄×D₃₉

Splittings

Fitting	C₃×C₄×C₁₃ ⋊ C₂
derived, Hall	C₃×C₁₃ ⋊ C₂×C₄
Sylow	C₁₃ ⋊ C₄×D₃
Sylow	C₃ ⋊ C₄×D₁₃

Subgroups

	subgroup	G/H
center, hypercenter	C₄	D₃₉
commutator, hypocenter	C₃×C₁₃	C₂×C₄
Frattini	C₂	C₂×D₃₉
Fitting	C₃×C₄×C₁₃	C₂
socle, cosocle	C₂×C₃×C₁₃	C₂²
prime radical	C₂×D₃₉	C₂
LCS	G ▷ C₃×C₁₃
UCS	C₁ ◁ C₄

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 20
transitive degree	μ_t(G) = 156

A minimal faithful permutation representation — 2 generators on 20 points:

(2,3)(4,5)(6,7)(8,9)(10,11)(12,13)(15,16);(1,2,4,6,8,10,12,13,11,9,7,5,3)(14,15,16)(17,18,19,20)

Conjugacy classes & character table

84 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	#10597591, #10597594, C₈×D₃₉, …
maximal normal subgroup of	#10597591, #10597594, C₈×D₃₉, …
maximal quotient of	C₈×D₃₉, #10597657, C₄×Dic₃₉, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(312, 38);