C₁₃×#904 #11928880

order	1248
isoclinism	isoclinic class of #204
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₃ · Schur multiplier (H₂) = C₂²

supersolvable
metabelian
solvable
monomial

Aliases

direct product

C₁₃×#904

Splittings

Fitting	C₂×C₃×C₈×C₁₃ ⋊ C₂
Hall	C₃×C₁₃ ⋊ #135
Sylow	C₃ ⋊ C₁₃×#135

Subgroups

	subgroup	G/H
center	C₄×C₁₃	D₁₂
commutator, cosocle	C₃×C₄	C₂³×C₁₃
Frattini	C₄	C₂²×D₃×C₁₃
Fitting	C₂×C₃×C₈×C₁₃	C₂
socle	C₂×C₃×C₁₃	C₂×D₄
hypercenter	C₂×C₈×C₁₃	D₃
hypocenter	C₃	C₁₃×#135
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₄×C₁₃ ◁ C₂×C₄×C₁₃ ◁ C₂×C₈×C₁₃

124 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 32
transitive degree	μ_t(G) = 624

A minimal faithful permutation representation — 3 generators on 32 points:

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

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1248, 992);

C13×#904 #11928880