D₁₂₁₈₇ #37567147

order	24374
automorphism	?
homology	Abelianization (H₁) = C₂ · Schur multiplier (H₂) = C₁

Aliases

dihedral	D₁₂₁₈₇
unambiguous semidirect product	C₇⋊D₁₇₄₁
unambiguous semidirect product	C₁₇₄₁⋊D₇

Splittings

Fitting, socle, derived, Hall	C₇×C₁₇₄₁ ⋊ C₂
Sylow	C₁₇₄₁ ⋊ D₇
Sylow	C₇ ⋊ D₁₇₄₁

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₇×C₁₇₄₁	C₂
LCS	G ▷ C₇×C₁₇₄₁
UCS	C₁

8 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 1748
transitive degree	μ_t(G) = 12187

A minimal faithful permutation representation — 2 generators on 1748 points:

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Polycyclic presentation:

2,7,1741|b^a=b^6,c^a=c^1740

Conjugacy classes & character table

6095 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24374, 3);

D12187 #37567147