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D₇×#465 #11738100

order	896
automorphism	?
homology	Abelianization (H₁) = C₂⁴ · Schur multiplier (H₂) = C₂⁵

Aliases

Splittings

Fitting	C₇×#465 ⋊ C₂
Sylow	C₇ ⋊ C₂×#465

Subgroups

	subgroup	G/H
center	C₂²	C₂×D₄×D₇
commutator, cosocle	C₂×C₄×C₇	C₂⁴
Frattini	C₂×C₄	C₂³×D₇
Fitting	C₇×#465	C₂
socle	C₂²×C₇	C₂²×D₄
prime radical	D₇×#121	C₂
hypercenter	#465	D₇
hypocenter	C₇	C₂×#465
LCS	G ▷ C₂×C₄×C₇ ▷ C₂×C₇ ▷ C₇
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #465

564 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 224

Conjugacy classes & character table

110 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂×D₇×#465, D₇×#3050, D₇×#3055, …
maximal normal subgroup of	C₂×D₇×#465, D₇×#3050, D₇×#3055, …
maximal quotient of	D₇×#1665, D₇×#1671, D₇×#1677, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(896, 12866);