Finite Group Databasebeta

C2×D4×Dic218 #28376506

order13952
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C29

Aliases

direct productC2×D4×Dic218

Splittings

SylowC109 ⋊ C2×D4×Q8

Subgroups

subgroupG/H
centerC23C23×D109
commutator, cosocleC22×C109C25
FrattiniC22C24×D109
FittingC2×C4×D4×C109C2
socleC23×C109C24
prime radicalC22×D4×C109C22
hypercenterC2×C4×D4D109
hypocenterC109C2×D4×Q8
LCSG ▷ C22×C109 ▷ C109
UCSC1 ◁ C23 ◁ C2×C4×D4

1568 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6976

Conjugacy classes & character table

2210 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13952, 17984);