Finite Group Databasebeta

C2×#14557393 #17996969

order4736
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C27

Aliases

direct productC2×#14557393

Splittings

SylowC37 ⋊ C2×#380

Subgroups

subgroupG/H
centerC24C22×D37
commutatorC22×C37C23×C4
FrattiniC23C23×D37
FittingC24×C4×C37C2
socleC24×C37C23
prime radicalC25×C37C22
cosocleC23×C37C24
hypercenterC24×C4D37
hypocenterC37C2×#380
LCSG ▷ C22×C37 ▷ C37
UCSC1 ◁ C24 ◁ C24×C4

1232 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2368

Conjugacy classes & character table

1208 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 6883);