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C₃×D₇×D₂₅ #14523544

order	2100
isoclinism	isoclinic class of D₇×D₂₅
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃ · Schur multiplier (H₂) = C₂

Aliases

C₃×D₇×D₂₅

Splittings

Fitting, Hall	C₃×C₇×C₂₅ ⋊ C₂²
derived, Hall	C₇×C₂₅ ⋊ C₂²×C₃
Hall	C₃×C₂₅ ⋊ C₂×D₇
Sylow	C₂₅ ⋊ C₂×C₃×D₇
Hall	C₃×C₇ ⋊ C₂×D₂₅
Sylow	C₇ ⋊ C₂×C₃×D₂₅

Subgroups

	subgroup	G/H
center, hypercenter	C₃	D₇×D₂₅
commutator, cosocle, hypocenter	C₇×C₂₅	C₂²×C₃
Frattini	C₅	C₃×D₅×D₇
Fitting	C₃×C₇×C₂₅	C₂²
socle	C₃×C₅×C₇	C₂×D₅
LCS	G ▷ C₇×C₂₅
UCS	C₁ ◁ C₃

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 35
transitive degree	μ_t(G) = 525

Conjugacy classes & character table

210 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₃×D₂₅×D₄₉, D₇×ΓL(1,𝔽₈)⋊D₂₅, (ΓL(1,𝔽₈)⋊D₇)⋊D₂₅, …
maximal normal subgroup of	C₃×C₇×D₇×D₂₅, C₃×C₁₁×D₇×D₂₅, C₃×C₁₃×D₇×D₂₅, …
maximal quotient of	C₃×D₂₅×D₄₉, D₇×ΓL(1,𝔽₈)⋊D₂₅, (ΓL(1,𝔽₈)⋊D₇)⋊D₂₅, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2100, 24);