Finite Group Databasebeta

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C₃×C₃₇₃⋊C₉ #23758555

order	10071
automorphism	?
homology	Abelianization (H₁) = C₃×C₉ · Schur multiplier (H₂) = C₃

Aliases

direct product	C₃×C₃₇₃⋊C₉
unambiguous semidirect product	(C₃×C₃₇₃)⋊C₉

Splittings

C₃₇₃ ⋊ C₃×C₉

Subgroups

	subgroup	G/H
center, hypercenter	C₃²	C₃₇₃⋊C₃
commutator, hypocenter	C₃₇₃	C₃×C₉
Frattini	C₃	C₃×C₃₇₃⋊C₃
Fitting, socle, prime radical	C₃²×C₃₇₃	C₃
cosocle	C₃×C₃₇₃	C₃²
LCS	G ▷ C₃₇₃
UCS	C₁ ◁ C₃²

20 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1143 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₉×C₃₇₃⋊C₉, (C₃×C₃₇₃⋊C₃)⋊C₉, C₃²⋊(C₃₇₃⋊C₉), …
maximal normal subgroup of	C₉×C₃₇₃⋊C₉, (C₃×C₃₇₃⋊C₃)⋊C₉, C₃²⋊(C₃₇₃⋊C₉), …
maximal quotient of	C₉×C₃₇₃⋊C₉, C₃²⋊(C₃₇₃⋊C₉), #44475071, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10071, 8);