Finite Group Databasebeta

C2×C22⋊C8×D109 #28371462

order13952
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C27

Aliases

direct productC2×C22⋊C8×D109

Splittings

FittingC2×C22⋊C8×C109 ⋊ C2
SylowC109 ⋊ C22×C22⋊C8

Subgroups

subgroupG/H
centerC22×C4C22×D109
commutatorC2×C109C23×C8
FrattiniC2×C4C23×D109
FittingC2×C22⋊C8×C109C2
socleC23×C109C22×C4
prime radicalC24×D109C4
cosocleC2×C4×C109C24
hypercenterC2×C22⋊C8D109
hypocenterC109C22×C22⋊C8
LCSG ▷ C2×C109 ▷ C109
UCSC1 ◁ C22×C4 ◁ C2×C22⋊C8

1072 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, 12940);