Finite Group Databasebeta

C2×#20294780 #28362722

order13952
automorphism?
homologyAbelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C25

Aliases

direct productC2×#20294780

Splittings

SylowC109 ⋊ C2×#336

Subgroups

subgroupG/H
centerC23×C4C2×D109
commutatorC2×C109C2×C4×C8
FrattiniC22×C4C22×D109
FittingC23×C8×C109C2
socle, prime radicalC24×C109C2×C4
cosocleC22×C4×C109C23
hypercenterC23×C8D109
hypocenterC109C2×#336
LCSG ▷ C2×C109 ▷ C109
UCSC1 ◁ C23×C4 ◁ C23×C8

528 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, 4200);