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D₄×Dic₁₃ #88188

order	416
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄ · Schur multiplier (H₂) = C₂³

Aliases

D₄×Dic₁₃

Splittings

C₁₃ ⋊ C₄×D₄

Subgroups

	subgroup	G/H
center, Frattini	C₂²	C₂²×D₁₃
commutator	C₂×C₁₃	C₂²×C₄
Fitting, prime radical	C₂×D₄×C₁₃	C₂
socle, cosocle	C₂²×C₁₃	C₂³
hypercenter	C₂×D₄	D₁₃
hypocenter	C₁₃	C₄×D₄
LCS	G ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ C₂×D₄

94 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 21
transitive degree	μ_t(G) = 208

A minimal faithful permutation representation — 3 generators on 21 points:

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

Conjugacy classes & character table

80 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	D₄⋊#1057, #11718417, #11718418, …
maximal normal subgroup of	D₄⋊#1057, #11718417, #11718418, …
maximal quotient of	C₂²⋊C₄×Dic₁₃, #11718611, #11718612, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(416, 155);