Finite Group Databasebeta

← Prev (#27134753) Next (#27134755) →

C₄⋊C₁₆×C₁₉₃ #27134754

order	12352
nilpotency class	2
isoclinism	isoclinic class of D₄
automorphism	?
homology	Abelianization (H₁) = C₂×C₁₆×C₁₉₃ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₄⋊C₁₆×C₁₉₃
unambiguous semidirect product	C₄⋊(C₁₆×C₁₉₃)

Subgroups

	subgroup	G/H
center	C₂×C₈×C₁₉₃	C₂²
commutator	C₂	C₂×C₁₆×C₁₉₃
Frattini, cosocle	C₂×C₈	C₂²×C₁₉₃
socle, prime radical	C₂²×C₁₉₃	C₂×C₈
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₈×C₁₉₃ ◁ G

50 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

7720 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	D₄⋊C₁₆×C₁₉₃, #1330×C₁₉₃, Q₈⋊C₁₆×C₁₉₃, …
maximal normal subgroup of	D₄⋊C₁₆×C₁₉₃, #1330×C₁₉₃, Q₈⋊C₁₆×C₁₉₃, …
maximal quotient of	#1367×C₁₉₃, #1370×C₁₉₃, #1374×C₁₉₃, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12352, 44);