Finite Group Databasebeta

← Prev (#43242145) Next (#43242147) →

C11×C49×Dic13 #43242146

order28028
automorphism?
homologyAbelianization (H1) = C4×C11×C49 · Schur multiplier (H2) = C1

Aliases

direct productC11×C49×Dic13

Splittings

derived, SylowC13 ⋊ C4×C11×C49
HallC11×C13×C49 ⋊ C4
HallC13×C49 ⋊ C4×C11
HallC11×C13 ⋊ C4×C49

Subgroups

subgroupG/H
center, hypercenterC2×C11×C49D13
commutator, hypocenterC13C4×C11×C49
FrattiniC2×C7C7×C11×D13
FittingC2×C11×C13×C49C2
socle, prime radicalC2×C7×C11×C13C2×C7
cosocleC2×C7×C13C2×C7×C11
LCSG ▷ C13
UCSC1 ◁ C2×C11×C49

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 28028

Conjugacy classes & character table

8624 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(28028, 2);