Finite Group Databasebeta

← Prev (#37566503) Next (#37566505) →

C₂×C₇⋊C₉×C₁₉₃ #37566504

order	24318
automorphism	?
homology	Abelianization (H₁) = C₂×C₉×C₁₉₃ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₂×C₇⋊C₉×C₁₉₃
unambiguous semidirect product	(C₂×C₇)⋊(C₉×C₁₉₃)

Splittings

derived, Sylow	C₇ ⋊ C₂×C₉×C₁₉₃
Hall	C₂×C₇×C₁₉₃ ⋊ C₉
Hall	C₇×C₁₉₃ ⋊ C₂×C₉
Hall	C₂×C₇ ⋊ C₉×C₁₉₃

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₃×C₁₉₃	ΓL(1,𝔽₈)
commutator, hypocenter	C₇	C₂×C₉×C₁₉₃
Frattini	C₃	C₂×ΓL(1,𝔽₈)×C₁₉₃
Fitting, socle, prime radical	C₂×C₃×C₇×C₁₉₃	C₃
cosocle	C₃×C₇	C₂×C₃×C₁₉₃
LCS	G ▷ C₇
UCS	C₁ ◁ C₂×C₃×C₁₉₃

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 24318

Conjugacy classes & character table

5790 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24318, 3);