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#41×D₁₃ #88255

order	416
automorphism	?
homology	Abelianization (H₁) = C₂⁴ · Schur multiplier (H₂) = C₂⁵

Aliases

#41×D₁₃

Splittings

Fitting	C₁₃×#41 ⋊ C₂
Sylow	C₁₃ ⋊ C₂×#41

Subgroups

	subgroup	G/H
center	C₄	C₂²×D₁₃
commutator, socle, cosocle	C₂×C₁₃	C₂⁴
Frattini	C₂	C₂³×D₁₃
Fitting	C₁₃×#41	C₂
hypercenter	#41	D₁₃
hypocenter	C₁₃	C₂×#41
LCS	G ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₄ ◁ #41

164 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

A minimal faithful permutation representation — 4 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)(14,16,17,20)(15,19,18,21);(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	D₁₃×#104, #11718482, D₁₃⋊#104, …
maximal normal subgroup of	D₁₃×#104, #11718482, D₁₃⋊#104, …
maximal quotient of	#11719222, D₁₃×#117, #11719227, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(416, 222);