Finite Group Databasebeta

C4×#16812730 #28371851

order13952
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC4×#16812730

Splittings

FittingC2×C4×Q8×C109 ⋊ C2
SylowC109 ⋊ C4×#137

Subgroups

subgroupG/H
centerC2×C4C2×C22⋊D109
commutatorC4×C109C23×C4
FrattiniC2×C4C23×D109
FittingC2×C4×Q8×C109C2
socleC22×C109C22×D4
prime radicalC2×#13182029C22
cosocleC2×C4×C109C24
hypercenterC2×C4×Q8D109
hypocenterC109C4×#137
LCSG ▷ C4×C109 ▷ C2×C109 ▷ C109
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C2×C4×Q8

484 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6976

Conjugacy classes & character table

2204 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13952, 13329);