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C₂×C₄×Dic₁₃ #88176

order	416
isoclinism	isoclinic class of D₁₃
automorphism	?
homology	Abelianization (H₁) = C₂×C₄² · Schur multiplier (H₂) = C₂²×C₄

Aliases

C₂×C₄×Dic₁₃

Splittings

C₁₃ ⋊ C₂×C₄²

Subgroups

	subgroup	G/H
center, hypercenter	C₂²×C₄	D₁₃
commutator, hypocenter	C₁₃	C₂×C₄²
Frattini	C₂²	C₂²×D₁₃
Fitting	C₂²×C₄×C₁₃	C₂
socle, prime radical	C₂³×C₁₃	C₂²
cosocle	C₂²×C₁₃	C₂³
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₂²×C₄

108 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 23
transitive degree	μ_t(G) = 416

A minimal faithful permutation representation — 3 generators on 23 points:

(1,2)(3,4,5,6)(12,13)(14,15)(16,17)(18,19)(20,21)(22,23);(7,8,9,10)(11,12,14,16,18,20,22,23,21,19,17,15,13);(1,2)

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	#11718124, #11718142, #11718147, …
maximal normal subgroup of	#11718124, #11718142, #11718147, …
maximal quotient of	C₂×C₄×#1055, C₂×#88043, C₄×#6099, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(416, 143);