Finite Group Databasebeta

← Prev (#64623) Next (#64625) →

C₂×Dic₃₉ #64624

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

Aliases

direct product	C₂×Dic₃₉
unambiguous semidirect product	(C₂×C₃)⋊Dic₁₃

Splittings

derived, Hall	C₃×C₁₃ ⋊ C₂×C₄
Sylow	C₁₃ ⋊ C₂×Dic₃
Sylow	C₃ ⋊ C₂×Dic₁₃

Subgroups

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

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 22
transitive degree	μ_t(G) = 312

A minimal faithful permutation representation — 2 generators on 22 points:

(1,2)(4,5)(6,7,8,9)(11,12)(13,14)(15,16)(17,18)(19,20)(21,22);(1,2)(3,4,5)(10,11,13,15,17,19,21,22,20,18,16,14,12)

Conjugacy classes & character table

84 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	Dic₃×Dic₁₃, #10597608, (C₂×D₃)⋊Dic₁₃, …
maximal normal subgroup of	Dic₃×Dic₁₃, #10597608, (C₂×D₃)⋊Dic₁₃, …
maximal quotient of	C₂×C₃⋊#1055, #10597662, C₄×Dic₃₉, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(312, 40);