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C₂×C₅⋊D₅×C₇₉ #21463611

order	7900
isoclinism	isoclinic class of C₅⋊D₅
automorphism	?
homology	Abelianization (H₁) = C₂²×C₇₉ · Schur multiplier (H₂) = C₂×C₅

Aliases

direct product	C₂×C₅⋊D₅×C₇₉
unambiguous semidirect product	(C₂×C₅)⋊(D₅×C₇₉)

Splittings

Fitting, socle	C₂×C₅²×C₇₉ ⋊ C₂
derived, Sylow	C₅² ⋊ C₂²×C₇₉
Hall	C₅²×C₇₉ ⋊ C₂²

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₇₉	C₅⋊D₅
commutator, hypocenter	C₅²	C₂²×C₇₉
Frattini	C₁	G
Fitting, socle	C₂×C₅²×C₇₉	C₂
LCS	G ▷ C₅²
UCS	C₁ ◁ C₂×C₇₉

80 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2212 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×C₇₉×(C₅⋊D₅)⋊C₃, C₂×(C₅⋊D₅)⋊(C₇₉⋊C₃), C₂×C₅⋊D₅×C₇₉⋊C₃, …
maximal normal subgroup of	C₂×C₇₉×(C₅⋊D₅)⋊C₃, C₂×(C₅⋊D₅)⋊(C₇₉⋊C₃), C₂×C₅⋊D₅×C₇₉⋊C₃, …
maximal quotient of	D₃×C₅⋊D₅×C₇₉, C₂×C₃×C₅⋊D₅×C₇₉, C₂×C₇₉×C₃⋊(C₅⋊D₅)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7900, 33);