Finite Group Databasebeta

← Prev (#11928876) Next (#11928878) →

C13×#901 #11928877

order1248
isoclinismisoclinic class of Dic6
automorphism?
homologyAbelianization (H1) = C22×C4×C13 · Schur multiplier (H2) = C22

Aliases

direct productC13×#901

Splittings

FittingC2×C3×C8×C13 ⋊ C2
HallC3×C13 ⋊ #131
SylowC3 ⋊ C13×#131

Subgroups

subgroupG/H
centerC8×C13C2×D3
commutatorC2×C3C22×C4×C13
FrattiniC4C22×D3×C13
FittingC2×C3×C8×C13C2
socleC2×C3×C13C22×C4
prime radicalC13×#235C2
cosocleC3×C4C23×C13
hypercenterC2×C8×C13D3
hypocenterC3C13×#131
LCSG ▷ C2×C3 ▷ C3
UCSC1 ◁ C8×C13 ◁ C2×C8×C13

124 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 32
transitive degreeμt(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)(17,19,20,25,21,26,27,31)(18,23,24,30,22,28,29,32);(18,22)(23,28)(24,29)(30,32);(15,16)(17,18)(19,23)(20,24)(21,22)(25,30)(26,28)(27,29)(31,32)

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1248, 989);