Finite Group Databasebeta

C2×C4×C8×D109 #28371431

order13952
isoclinismisoclinic class of D109
automorphism?
homologyAbelianization (H1) = C22×C4×C8 · Schur multiplier (H2) = C25×C4

Aliases

direct productC2×C4×C8×D109

Splittings

FittingC2×C4×C8×C109 ⋊ C2
derived, SylowC109 ⋊ C22×C4×C8

Subgroups

subgroupG/H
center, hypercenterC2×C4×C8D109
commutator, hypocenterC109C22×C4×C8
FrattiniC2×C4C23×D109
FittingC2×C4×C8×C109C2
socleC23×C109C22×C4
prime radicalC23×D109C2×C4
cosocleC2×C4×C109C24
LCSG ▷ C109
UCSC1 ◁ C2×C4×C8

760 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6976

Conjugacy classes & character table

3584 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13952, 12909);