Finite Group Databasebeta

← Prev (#37523816) Next (#37523818) →

C₂×C₁₉×C₆₇⋊C₉ #37523817

order	22914
automorphism	?
homology	Abelianization (H₁) = C₂×C₉×C₁₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₂×C₁₉×C₆₇⋊C₉
unambiguous semidirect product	(C₂×C₆₇)⋊(C₉×C₁₉)

Splittings

derived, Sylow	C₆₇ ⋊ C₂×C₉×C₁₉
Hall	C₂×C₁₉×C₆₇ ⋊ C₉
Hall	C₁₉×C₆₇ ⋊ C₂×C₉
Hall	C₂×C₆₇ ⋊ C₉×C₁₉

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₃×C₁₉	C₆₇⋊C₃
commutator, hypocenter	C₆₇	C₂×C₉×C₁₉
Frattini	C₃	C₂×C₁₉×C₆₇⋊C₃
Fitting, socle, prime radical	C₂×C₃×C₁₉×C₆₇	C₃
cosocle	C₃×C₆₇	C₂×C₃×C₁₉
LCS	G ▷ C₆₇
UCS	C₁ ◁ C₂×C₃×C₁₉

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 22914

Conjugacy classes & character table

2850 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22914, 2);