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Dic₅×C₃₄₉ #20296115

order	6980
isoclinism	isoclinic class of D₅
automorphism	?
homology	Abelianization (H₁) = C₄×C₃₄₉ · Schur multiplier (H₂) = C₁

Aliases

Dic₅×C₃₄₉

Splittings

derived, Sylow	C₅ ⋊ C₄×C₃₄₉
Hall	C₅×C₃₄₉ ⋊ C₄

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₃₄₉	D₅
commutator, hypocenter	C₅	C₄×C₃₄₉
Frattini	C₂	D₅×C₃₄₉
Fitting, socle	C₂×C₅×C₃₄₉	C₂
LCS	G ▷ C₅
UCS	C₁ ◁ C₂×C₃₄₉

12 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2792 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃×Dic₅×C₃₄₉, Dic₁₅×C₃₄₉, Dic₅×C₃₄₉⋊C₃, …
maximal normal subgroup of	C₃×Dic₅×C₃₄₉, Dic₅×C₃₄₉⋊C₃, C₅×Dic₅×C₃₄₉
maximal quotient of	C₃×Dic₅×C₃₄₉, Dic₁₅×C₃₄₉, Dic₂₅×C₃₄₉, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(6980, 2);