Finite Group Databasebeta

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D₇×#3717 #72245809

order	2016
automorphism	?
homology	Abelianization (H₁) = C₂³ · Schur multiplier (H₂) = C₂²

Aliases

Splittings

Hall	C₃²×C₇ ⋊ C₂×SD₁₆
Sylow	C₃² ⋊ D₇×SD₁₆
Sylow	C₇ ⋊ C₂×#3717

Subgroups

	subgroup	G/H
center	C₂	D₇×#626
commutator, Fitting, cosocle	C₃²×C₄×C₇	C₂³
Frattini, hypercenter	C₄	D₃²×D₇
socle	C₂×C₃²×C₇	C₂×D₄
prime radical	D₇×C₄⋊(C₃⋊D₃)	C₂
hypocenter	C₃²×C₇	C₂×SD₁₆
LCS	G ▷ C₃²×C₄×C₇ ▷ C₂×C₃²×C₇ ▷ C₃²×C₇
UCS	C₁ ◁ C₂ ◁ C₄

326 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 326 conjugacy classes of subgroups — too many to draw. Only its 70 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 168

Conjugacy classes & character table

120 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	D₇×#63930, D₇×#63937, D₇×#63825, …
maximal normal subgroup of	D₇×#63930, D₇×#63937, D₇×#63825, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.