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C₃×D₃×D₇×C₂₉ #20300649

order	7308
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃×C₂₉ · Schur multiplier (H₂) = C₂

Aliases

C₃×D₃×D₇×C₂₉

Splittings

Fitting, socle, Hall	C₃²×C₇×C₂₉ ⋊ C₂²
derived	C₃×C₇ ⋊ C₂²×C₃×C₂₉
Hall	C₃²×C₂₉ ⋊ C₂×D₇
Hall	C₇×C₂₉ ⋊ C₂×C₃×D₃
Hall	C₃²×C₇ ⋊ C₂²×C₂₉
Sylow	C₃² ⋊ C₂×D₇×C₂₉
Sylow	C₇ ⋊ C₂×C₃×D₃×C₂₉

Subgroups

	subgroup	G/H
center, hypercenter	C₃×C₂₉	D₃×D₇
commutator, hypocenter	C₃×C₇	C₂²×C₃×C₂₉
Frattini	C₁	G
Fitting, socle	C₃²×C₇×C₂₉	C₂²
LCS	G ▷ C₃×C₇
UCS	C₁ ◁ C₃×C₂₉

88 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1305 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃×C₅×D₃×D₇×C₂₉, C₃×D₇×C₂₉×D₁₅, C₃×D₃×C₂₉×D₃₅, …
maximal normal subgroup of	C₃×C₅×D₃×D₇×C₂₉
maximal quotient of	C₃×C₅×D₃×D₇×C₂₉, C₃×D₇×C₂₉×D₁₅, C₃×D₃×C₂₉×D₃₅, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7308, 124);