C₃²×C₁₉⋊C₈ #13062948

order	1368
isoclinism	isoclinic class of D₁₉
automorphism	?
homology	Abelianization (H₁) = C₃²×C₈ · Schur multiplier (H₂) = C₃

Aliases

direct product

C₃²×C₁₉⋊C₈

Splittings

derived, Sylow	C₁₉ ⋊ C₃²×C₈
Hall	C₃²×C₁₉ ⋊ C₈

Subgroups

	subgroup	G/H
center, hypercenter	C₃²×C₄	D₁₉
commutator, hypocenter	C₁₉	C₃²×C₈
Frattini	C₄	C₃²×D₁₉
Fitting	C₃²×C₄×C₁₉	C₂
socle, prime radical	C₂×C₃²×C₁₉	C₄
cosocle	C₄×C₁₉	C₂×C₃²
LCS	G ▷ C₁₉
UCS	C₁ ◁ C₃²×C₄

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 33
transitive degree	μ_t(G) = 1368

A minimal faithful permutation representation — 2 generators on 33 points:

(1,2,3)(8,9)(10,11)(12,13)(14,15)(16,17)(18,19)(20,21)(22,23)(24,25)(26,27,28,30,29,31,32,33);(4,5,6)(7,8,10,12,14,16,18,20,22,24,25,23,21,19,17,15,13,11,9)

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1368, 48);

C32×C19⋊C8 #13062948