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D₇×#11765919 #30630692

order	16002
automorphism	?
homology	Abelianization (H₁) = C₂×C₉ · Schur multiplier (H₂) = C₁

Aliases

D₇×#11765919

Splittings

Fitting, socle, derived, Hall	C₇×C₁₂₇ ⋊ C₂×C₉
Hall	C₇×#11765919 ⋊ C₂
Hall	D₇×C₁₂₇ ⋊ C₉
Sylow	C₁₂₇ ⋊ C₉×D₇
Sylow	C₇ ⋊ C₂×#11765919

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₇×C₁₂₇	C₂×C₉
prime radical	D₇×C₁₂₇⋊C₃	C₃
cosocle	C₇×C₁₂₇⋊C₃	C₂×C₃
LCS	G ▷ C₇×C₁₂₇
UCS	C₁

24 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

115 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	D₇×#11765919⋊C₂, C₂×D₇×#11765919
maximal normal subgroup of	D₇×#11765919⋊C₂, C₂×D₇×#11765919
maximal quotient of	Dic₇×#11765919, C₂×D₇×#11765919

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16002, 49);