Finite Group Databasebeta

C2×#20294789 #28362746

order13952
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C25

Aliases

direct productC2×#20294789

Splittings

SylowC109 ⋊ C2×#340

Subgroups

subgroupG/H
centerC24D436
commutatorC4×C109C2×C42
FrattiniC22×C4C22×D109
FittingC23×C8×C109C2
socle, prime radicalC24×C109D4
cosocleC22×C4×C109C23
hypercenterC23×C8D109
hypocenterC109C2×#340
LCSG ▷ C4×C109 ▷ C2×C109 ▷ C109
UCSC1 ◁ C24 ◁ C23×C4 ◁ C23×C8

512 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 13952

Conjugacy classes & character table

3512 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13952, 4224);