Finite Group Databasebeta

C2×C4×#13182032 #28379228

order13952
automorphism?
homologyAbelianization (H1) = C2×C4×C16 · Schur multiplier (H2) = C22×C4

Aliases

direct productC2×C4×#13182032

Splittings

derived, SylowC109 ⋊ C2×C4×C16

Subgroups

subgroupG/H
center, hypercenterC2×C42#89137
commutator, hypocenterC109C2×C4×C16
FrattiniC2×C4C22×#89137
FittingC2×C42×C109C4
socle, prime radicalC23×C109C2×C8
cosocleC2×#11724784C23
LCSG ▷ C109
UCSC1 ◁ C2×C42

216 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 13952

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13952, 20706);