Finite Group Databasebeta

C8×D4×D109 #28371701

order13952
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C26

Aliases

direct productC8×D4×D109

Splittings

FittingC8×D4×C109 ⋊ C2
SylowC109 ⋊ C2×C8×D4

Subgroups

subgroupG/H
centerC2×C8C22×D109
commutatorC2×C109C23×C8
FrattiniC2×C4C23×D109
FittingC8×D4×C109C2
socleC22×C109C23×C4
prime radicalC2×D4×D109C4
cosocleC2×C4×C109C24
hypercenterC8×D4D109
hypocenterC109C2×C8×D4
LCSG ▷ C2×C109 ▷ C109
UCSC1 ◁ C2×C8 ◁ C8×D4

616 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3488

Conjugacy classes & character table

2240 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13952, 13179);