Finite Group Databasebeta

C4×#16812664 #28365381

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

Aliases

direct productC4×#16812664

Splittings

SylowC109 ⋊ C42×Q8

Subgroups

subgroupG/H
centerC22×C4C22×D109
commutatorC2×C109C22×C42
FrattiniC23C23×D109
FittingC4×C4⋊C4×C109C2
socle, prime radical, cosocleC23×C109C24
hypercenterC4×C4⋊C4D109
hypocenterC109C42×Q8
LCSG ▷ C2×C109 ▷ C109
UCSC1 ◁ C22×C4 ◁ C4×C4⋊C4

684 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 13952

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, 6859);