D₁₂₂₂₉ #37587403

order	24458
automorphism	?
homology	Abelianization (H₁) = C₂ · Schur multiplier (H₂) = C₁

Aliases

dihedral	D₁₂₂₂₉
unambiguous semidirect product	C₇⋊D₁₇₄₇
unambiguous semidirect product	C₁₇₄₇⋊D₇

Splittings

Fitting, socle, derived, Hall	C₇×C₁₇₄₇ ⋊ C₂
Sylow	C₁₇₄₇ ⋊ D₇
Sylow	C₇ ⋊ D₁₇₄₇

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₇×C₁₇₄₇	C₂
LCS	G ▷ C₇×C₁₇₄₇
UCS	C₁

8 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 1754
transitive degree	μ_t(G) = 12229

A minimal faithful permutation representation — 2 generators on 1754 points:

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Polycyclic presentation:

2,7,1747|b^a=b^6,c^a=c^1746

Conjugacy classes & character table

6116 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24458, 3);

D12229 #37587403