Finite Group Databasebeta

C2×C3×Dic52 #11928795

order1248
isoclinismisoclinic class of #6095
automorphism?
homologyAbelianization (H1) = C23×C3 · Schur multiplier (H2) = C22

Aliases

direct productC2×C3×Dic52

Splittings

HallC3×C13 ⋊ C2×Q16
SylowC13 ⋊ C2×C3×Q16

Subgroups

subgroupG/H
centerC22×C3D52
commutator, cosocleC4×C13C23×C3
FrattiniC4C22×C3×D13
FittingC2×C3×C8×C13C2
socle, prime radicalC22×C3×C13D4
hypercenterC2×C3×C8D13
hypocenterC13C2×C3×Q16
LCSG ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22×C3 ◁ C2×C3×C4 ◁ C2×C3×C8

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1248

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1248, 907);