Finite Group Databasebeta

C4×#16812609 #28362716

order13952
automorphism?
homologyAbelianization (H1) = C43 · Schur multiplier (H2) = C2×C42

Aliases

direct productC4×#16812609

Splittings

SylowC109 ⋊ C4×#97

Subgroups

subgroupG/H
centerC2×C42C2×D109
commutatorC2×C109C43
FrattiniC22×C4C22×D109
FittingC2×C4×C8×C109C2
socle, prime radicalC23×C109C22×C4
cosocleC22×C4×C109C23
hypercenterC2×C4×C8D109
hypocenterC109C4×#97
LCSG ▷ C2×C109 ▷ C109
UCSC1 ◁ C2×C42 ◁ C2×C4×C8

360 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 13952

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, 4194);