D₁₅₂₃₇ #44478706

order	30474
automorphism	?
homology	Abelianization (H₁) = C₂ · Schur multiplier (H₂) = C₁

Aliases

dihedral	D₁₅₂₃₇
unambiguous semidirect product	C₉⋊D₁₆₉₃
unambiguous semidirect product	C₁₆₉₃⋊D₉

Splittings

Fitting, derived, Hall	C₉×C₁₆₉₃ ⋊ C₂
Sylow	C₁₆₉₃ ⋊ D₉
Sylow	C₉ ⋊ D₁₆₉₃

Subgroups

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	C₉×C₁₆₉₃	C₂
Frattini	C₃	D₅₀₇₉
socle	C₃×C₁₆₉₃	D₃
LCS	G ▷ C₉×C₁₆₉₃
UCS	C₁

12 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 1702
transitive degree	μ_t(G) = 15237

A minimal faithful permutation representation — 2 generators on 1702 points:

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Polycyclic presentation:

2,3,1693,3|b^3=d^2,b^a=b^2d,c^a=c^1692,d^a=d^2

Conjugacy classes & character table

7620 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×D₁₅₂₃₇
maximal normal subgroup of	C₂×D₁₅₂₃₇
maximal quotient of	Dic₁₅₂₃₇, C₂×D₁₅₂₃₇

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30474, 6);

D15237 #44478706