Finite Group Databasebeta

C2×#20295148 #28371928

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

Aliases

direct productC2×#20295148

Splittings

SylowC109 ⋊ C2×#444

Subgroups

subgroupG/H
centerC2×C4D4×D109
commutatorC4×C109C23×C4
FrattiniC2×C4C23×D109
Fitting, prime radicalC2×#135×C109C2
socleC22×C109C4×D4
cosocleC2×C4×C109C24
hypercenterC2×#135D109
hypocenterC109C2×#444
LCSG ▷ C4×C109 ▷ C2×C109 ▷ C109
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×#135

464 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3488

Conjugacy classes & character table

1556 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13952, 13406);