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D₇×D₃₂ #11727129

order	896
automorphism	?
homology	Abelianization (H₁) = C₂³ · Schur multiplier (H₂) = C₂³

Aliases

D₇×D₃₂

Splittings

Fitting	C₇×D₃₂ ⋊ C₂
Sylow	C₇ ⋊ C₂×D₃₂

Subgroups

	subgroup	G/H
center	C₂	D₇×D₁₆
commutator, cosocle	C₇×C₁₆	C₂³
Frattini	C₁₆	C₂²×D₇
Fitting	C₇×D₃₂	C₂
socle	C₂×C₇	C₂×D₁₆
hypercenter	D₃₂	D₇
hypocenter	C₇	C₂×D₃₂
LCS	G ▷ C₇×C₁₆ ▷ C₇×C₈ ▷ C₄×C₇ ▷ C₂×C₇ ▷ C₇
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ C₁₆ ◁ D₃₂

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 224

Conjugacy classes & character table

95 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	D₇×D₆₄, D₇×SD₁₂₈, #13274852, …
maximal normal subgroup of	D₇×D₆₄, D₇×SD₁₂₈, #13274852, …
maximal quotient of	D₇×#1415, D₇×#1423, #13274367, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(896, 1895);