D₁₂₅₂₃ #38736740

order	25046
automorphism	?
homology	Abelianization (H₁) = C₂ · Schur multiplier (H₂) = C₁

Aliases

dihedral	D₁₂₅₂₃
unambiguous semidirect product	C₇⋊D₁₇₈₉
unambiguous semidirect product	C₁₇₈₉⋊D₇

Splittings

Fitting, socle, derived, Hall	C₇×C₁₇₈₉ ⋊ C₂
Sylow	C₁₇₈₉ ⋊ D₇
Sylow	C₇ ⋊ D₁₇₈₉

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₇×C₁₇₈₉	C₂
LCS	G ▷ C₇×C₁₇₈₉
UCS	C₁

8 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 1796
transitive degree	μ_t(G) = 12523

A minimal faithful permutation representation — 2 generators on 1796 points:

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Polycyclic presentation:

2,7,1789|b^a=b^6,c^a=c^1788

Conjugacy classes & character table

6263 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×D₁₂₅₂₃
maximal normal subgroup of	C₂×D₁₂₅₂₃
maximal quotient of	Dic₁₂₅₂₃, C₂×D₁₂₅₂₃

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25046, 3);

D12523 #38736740