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M₁₆×D₁₃ #88160

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

Aliases

M₁₆×D₁₃

Splittings

Fitting	C₁₃×M₁₆ ⋊ C₂
Sylow	C₁₃ ⋊ C₂×M₁₆

Subgroups

	subgroup	G/H
center, Frattini	C₄	C₂²×D₁₃
commutator, socle	C₂×C₁₃	C₂²×C₄
Fitting	C₁₃×M₁₆	C₂
prime radical	C₂²×D₁₃	C₄
cosocle	C₄×C₁₃	C₂³
hypercenter	M₁₆	D₁₃
hypocenter	C₁₃	C₂×M₁₆
LCS	G ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₄ ◁ M₁₆

68 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 21
transitive degree	μ_t(G) = 104

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

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

Conjugacy classes & character table

80 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	#11718271, #11718272, #11718273, …
maximal normal subgroup of	#11718271, #11718272, #11718273, …
maximal quotient of	#11718362, D₁₃×#97, #11718366, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(416, 127);