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C₂×C₁₉₃⋊C₉ #16812437

order	3474
automorphism	?
homology	Abelianization (H₁) = C₂×C₉ · Schur multiplier (H₂) = C₁

Aliases

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

Splittings

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

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₃	C₁₉₃⋊C₃
commutator, hypocenter	C₁₉₃	C₂×C₉
Frattini	C₃	C₂×C₁₉₃⋊C₃
Fitting, socle, prime radical	C₂×C₃×C₁₉₃	C₃
cosocle	C₃×C₁₉₃	C₂×C₃
LCS	G ▷ C₁₉₃
UCS	C₁ ◁ C₂×C₃

12 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 204
transitive degree	μ_t(G) = 3474

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂×C₅×C₁₉₃⋊C₉, D₅×C₁₉₃⋊C₉, C₂×C₇×C₁₉₃⋊C₉, …
maximal normal subgroup of	C₂×C₅×C₁₉₃⋊C₉, C₂×C₇×C₁₉₃⋊C₉, C₂×C₁₁×C₁₉₃⋊C₉
maximal quotient of	C₂×C₅×C₁₉₃⋊C₉, D₅×C₁₉₃⋊C₉, C₂×C₇×C₁₉₃⋊C₉, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3474, 3);