D₁₂₂₇₁ #37589386

order	24542
automorphism	?
homology	Abelianization (H₁) = C₂ · Schur multiplier (H₂) = C₁

Aliases

dihedral	D₁₂₂₇₁
unambiguous semidirect product	C₇⋊D₁₇₅₃
unambiguous semidirect product	C₁₇₅₃⋊D₇

Splittings

Fitting, socle, derived, Hall	C₇×C₁₇₅₃ ⋊ C₂
Sylow	C₁₇₅₃ ⋊ D₇
Sylow	C₇ ⋊ D₁₇₅₃

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₇×C₁₇₅₃	C₂
LCS	G ▷ C₇×C₁₇₅₃
UCS	C₁

8 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 1760
transitive degree	μ_t(G) = 12271

A minimal faithful permutation representation — 2 generators on 1760 points:

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Polycyclic presentation:

2,7,1753|b^a=b^6,c^a=c^1752

Conjugacy classes & character table

6137 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24542, 3);

D12271 #37589386