D₁₂₉₂₉ #39905487

order	25858
automorphism	?
homology	Abelianization (H₁) = C₂ · Schur multiplier (H₂) = C₁

Aliases

dihedral	D₁₂₉₂₉
unambiguous semidirect product	C₇⋊D₁₈₄₇
unambiguous semidirect product	C₁₈₄₇⋊D₇

Splittings

Fitting, socle, derived, Hall	C₇×C₁₈₄₇ ⋊ C₂
Sylow	C₁₈₄₇ ⋊ D₇
Sylow	C₇ ⋊ D₁₈₄₇

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₇×C₁₈₄₇	C₂
LCS	G ▷ C₇×C₁₈₄₇
UCS	C₁

8 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 1854
transitive degree	μ_t(G) = 12929

A minimal faithful permutation representation — 2 generators on 1854 points:

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Polycyclic presentation:

2,7,1847|b^a=b^6,c^a=c^1846

Conjugacy classes & character table

6466 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×D₁₂₉₂₉
maximal normal subgroup of	C₂×D₁₂₉₂₉
maximal quotient of	Dic₁₂₉₂₉, C₂×D₁₂₉₂₉

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25858, 3);

D12929 #39905487