Finite Group Databasebeta

C4×#16812705 #28371452

order13952
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C4

Aliases

direct productC4×#16812705

Splittings

FittingC2×C4×C8×C109 ⋊ C2
SylowC109 ⋊ C4×#131

Subgroups

subgroupG/H
centerC4×C8C2×D109
commutatorC2×C109C22×C42
FrattiniC2×C4C23×D109
FittingC2×C4×C8×C109C2
socleC22×C109C23×C4
prime radicalC2×#13182029C22
cosocleC2×C4×C109C24
hypercenterC2×C4×C8D109
hypocenterC109C4×#131
LCSG ▷ C2×C109 ▷ C109
UCSC1 ◁ C4×C8 ◁ C2×C4×C8

572 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6976

Conjugacy classes & character table

3536 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13952, 12930);