D₁₂₇₆₁ #38784190

order	25522
automorphism	?
homology	Abelianization (H₁) = C₂ · Schur multiplier (H₂) = C₁

Aliases

dihedral	D₁₂₇₆₁
unambiguous semidirect product	C₇⋊D₁₈₂₃
unambiguous semidirect product	C₁₈₂₃⋊D₇

Splittings

Fitting, socle, derived, Hall	C₇×C₁₈₂₃ ⋊ C₂
Sylow	C₁₈₂₃ ⋊ D₇
Sylow	C₇ ⋊ D₁₈₂₃

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₇×C₁₈₂₃	C₂
LCS	G ▷ C₇×C₁₈₂₃
UCS	C₁

8 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 1830
transitive degree	μ_t(G) = 12761

A minimal faithful permutation representation — 2 generators on 1830 points:

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Polycyclic presentation:

2,7,1823|b^a=b^6,c^a=c^1822

Conjugacy classes & character table

6382 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×D₁₂₇₆₁
maximal normal subgroup of	C₂×D₁₂₇₆₁
maximal quotient of	Dic₁₂₇₆₁, C₂×D₁₂₇₆₁

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25522, 3);

D12761 #38784190