Finite Group Databasebeta

← Prev (#29506169) Next (#29506171) →

C₉×C₂₃×D₃₇ #29506170

order	15318
isoclinism	isoclinic class of D₃₇
automorphism	?
homology	Abelianization (H₁) = C₂×C₉×C₂₃ · Schur multiplier (H₂) = C₁

Aliases

C₉×C₂₃×D₃₇

Splittings

Fitting, Hall	C₉×C₂₃×C₃₇ ⋊ C₂
derived, Sylow	C₃₇ ⋊ C₂×C₉×C₂₃
Hall	C₂₃×C₃₇ ⋊ C₂×C₉
Hall	C₉×C₃₇ ⋊ C₂×C₂₃

Subgroups

	subgroup	G/H
center, hypercenter	C₉×C₂₃	D₃₇
commutator, hypocenter	C₃₇	C₂×C₉×C₂₃
Frattini	C₃	C₃×C₂₃×D₃₇
Fitting	C₉×C₂₃×C₃₇	C₂
socle	C₃×C₂₃×C₃₇	C₂×C₃
prime radical	C₃×C₂₃×D₃₇	C₃
cosocle	C₃×C₃₇	C₂×C₃×C₂₃
LCS	G ▷ C₃₇
UCS	C₁ ◁ C₉×C₂₃

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 7659

Conjugacy classes & character table

4140 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₉×C₂₃×#3866, C₉×C₂₃⋊#3866, C₉×D₂₃×D₃₇, …
maximal normal subgroup of	C₉×C₂₃×#3866, C₉×C₂₃⋊#3866, C₉×D₂₃×D₃₇, …
maximal quotient of	C₉×C₂₃×Dic₃₇, C₂×C₉×C₂₃×D₃₇

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15318, 3);