C₂×D₈₃₄₅ #45688796

order	33380
automorphism	?
homology	Abelianization (H₁) = C₂² · Schur multiplier (H₂) = C₂

Aliases

dihedral	D₁₆₆₉₀
direct product	C₂×D₈₃₄₅
unambiguous semidirect product	(C₂×C₅)⋊D₁₆₆₉
unambiguous semidirect product	(C₂×C₁₆₆₉)⋊D₅

Splittings

Fitting, socle	C₂×C₅×C₁₆₆₉ ⋊ C₂
derived, Hall	C₅×C₁₆₆₉ ⋊ C₂²
Sylow	C₁₆₆₉ ⋊ C₂×D₅
Sylow	C₅ ⋊ C₂×D₁₆₆₉

Subgroups

	subgroup	G/H
center, hypercenter	C₂	D₈₃₄₅
commutator, cosocle, hypocenter	C₅×C₁₆₆₉	C₂²
Frattini	C₁	G
Fitting, socle	C₂×C₅×C₁₆₆₉	C₂
LCS	G ▷ C₅×C₁₆₆₉
UCS	C₁ ◁ C₂

20 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 1676
transitive degree	μ_t(G) = 16690

A minimal faithful permutation representation — 2 generators on 1676 points:

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Conjugacy classes & character table

8348 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33380, 15);

C2×D8345 #45688796