D₁₂₅₀₉ #38736176

order	25018
automorphism	?
homology	Abelianization (H₁) = C₂ · Schur multiplier (H₂) = C₁

Aliases

dihedral	D₁₂₅₀₉
unambiguous semidirect product	C₇⋊D₁₇₈₇
unambiguous semidirect product	C₁₇₈₇⋊D₇

Splittings

Fitting, socle, derived, Hall	C₇×C₁₇₈₇ ⋊ C₂
Sylow	C₁₇₈₇ ⋊ D₇
Sylow	C₇ ⋊ D₁₇₈₇

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₇×C₁₇₈₇	C₂
LCS	G ▷ C₇×C₁₇₈₇
UCS	C₁

8 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 1794
transitive degree	μ_t(G) = 12509

A minimal faithful permutation representation — 2 generators on 1794 points:

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Polycyclic presentation:

2,7,1787|b^a=b^6,c^a=c^1786

Conjugacy classes & character table

6256 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×D₁₂₅₀₉
maximal normal subgroup of	C₂×D₁₂₅₀₉
maximal quotient of	Dic₁₂₅₀₉, C₂×D₁₂₅₀₉

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25018, 3);

D12509 #38736176