Finite Group Databasebeta

C2×C3×C4⋊Dic13 #11928815

order1248
isoclinismisoclinic class of Dic26
automorphism?
homologyAbelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C23

Aliases

direct productC2×C3×C4⋊Dic13

Splittings

HallC3×C13 ⋊ C2×C4⋊C4
SylowC13 ⋊ C2×C3×C4⋊C4

Subgroups

subgroupG/H
centerC23×C3C2×D13
commutatorC2×C13C22×C3×C4
FrattiniC22C22×C3×D13
FittingC22×C3×C4×C13C2
socle, prime radicalC23×C3×C13C22
cosocleC22×C13C23×C3
hypercenterC22×C3×C4D13
hypocenterC13C2×C3×C4⋊C4
LCSG ▷ C2×C13 ▷ C13
UCSC1 ◁ C23×C3 ◁ C22×C3×C4

184 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1248

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1248, 927);