Finite Group Databasebeta

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C₇×Dic₁₁₉₇ #45691535

order	33516
automorphism	?
homology	Abelianization (H₁) = C₄×C₇ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₇×Dic₁₁₉₇
unambiguous semidirect product	C₇⋊(C₇×Dic₁₇₁)
unambiguous semidirect product	C₉⋊(C₇×Dic₁₃₃)
unambiguous semidirect product	C₁₉⋊(C₇×Dic₆₃)

Splittings

derived	C₇×C₉×C₁₉ ⋊ C₄×C₇
Hall	C₇²×C₉×C₁₉ ⋊ C₄
Hall	C₇²×C₁₉ ⋊ Dic₉
Hall	C₇²×C₉ ⋊ Dic₁₉
Hall	C₉×C₁₉ ⋊ C₇×Dic₇
Sylow	C₇² ⋊ Dic₁₇₁
Sylow	C₁₉ ⋊ C₇×Dic₆₃
Sylow	C₉ ⋊ C₇×Dic₁₃₃

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₇	D₁₁₉₇
commutator, hypocenter	C₇×C₉×C₁₉	C₄×C₇
Frattini	C₂×C₃	C₇×D₃₉₉
Fitting	C₂×C₇²×C₉×C₁₉	C₂
socle, prime radical	C₂×C₃×C₇²×C₁₉	D₃
cosocle	C₂×C₇×C₉×C₁₉	C₂×C₇
LCS	G ▷ C₇×C₉×C₁₉
UCS	C₁ ◁ C₂×C₇

108 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 4788

Conjugacy classes & character table

8400 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33516, 333);