D₁₅₆₀₈ #44530167

order	31216
automorphism	?
homology	Abelianization (H₁) = C₂² · Schur multiplier (H₂) = C₂

Aliases

dihedral

D₁₅₆₀₈

Splittings

Fitting	C₈×C₁₉₅₁ ⋊ C₂
Sylow	C₁₉₅₁ ⋊ D₈

Subgroups

	subgroup	G/H
center	C₂	D₇₈₀₄
commutator, cosocle	C₄×C₁₉₅₁	C₂²
Frattini	C₄	C₂×D₁₉₅₁
Fitting	C₈×C₁₉₅₁	C₂
socle	C₂×C₁₉₅₁	D₄
hypercenter	C₈	D₁₉₅₁
hypocenter	C₁₉₅₁	D₈
LCS	G ▷ C₄×C₁₉₅₁ ▷ C₂×C₁₉₅₁ ▷ C₁₉₅₁
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈

22 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 1959
transitive degree	μ_t(G) = 15608

A minimal faithful permutation representation — 2 generators on 1959 points:

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Polycyclic presentation:

2^4,1951|c^2=d,b^a=bc,c^a=cd,e^a=e^1950,c^b=cd,e^b=e^1950

Conjugacy classes & character table

7807 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31216, 26);

D15608 #44530167