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D₇×C₅⋊D₈₅ #26045446

order	11900
automorphism	?
homology	Abelianization (H₁) = C₂² · Schur multiplier (H₂) = C₂×C₅

Aliases

direct product	D₇×C₅⋊D₈₅
unambiguous semidirect product	(C₅×D₇)⋊D₈₅
unambiguous semidirect product	(D₇×C₁₇)⋊(C₅⋊D₅)

Splittings

Fitting, socle, derived, Hall	C₅²×C₇×C₁₇ ⋊ C₂²
Hall	C₅²×C₁₇ ⋊ C₂×D₇
Hall	C₅²×C₇ ⋊ C₂×D₁₇
Hall	C₇×C₁₇ ⋊ C₂×C₅⋊D₅
Sylow	C₅² ⋊ D₇×D₁₇
Sylow	C₁₇ ⋊ D₇×C₅⋊D₅
Sylow	C₇ ⋊ C₂×C₅⋊D₈₅

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₅²×C₇×C₁₇	C₂²
LCS	G ▷ C₅²×C₇×C₁₇
UCS	C₁

160 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1070 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	D₇⋊(C₁₇⋊((C₅⋊D₅)⋊C₃)), D₇×C₁₇⋊((C₅⋊D₅)⋊C₃), AGL(1,𝔽₇)×C₅⋊D₈₅, …
maximal normal subgroup of	D₇⋊(C₁₇⋊((C₅⋊D₅)⋊C₃)), D₇×C₁₇⋊((C₅⋊D₅)⋊C₃), AGL(1,𝔽₇)×C₅⋊D₈₅, …
maximal quotient of	C₃×D₇×C₅⋊D₈₅, D₇×C₃⋊(C₅⋊D₈₅), D₂₁×C₅⋊D₈₅, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11900, 95);