Finite Group Databasebeta

C2×#14557413 #17997015

order4736
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C28

Aliases

direct productC2×#14557413

Splittings

SylowC37 ⋊ C2×#386

Subgroups

subgroupG/H
centerC24C22×D37
commutatorC22×C37C23×C4
FrattiniC23C23×D37
Fitting, prime radicalC23×D4×C37C2
socleC24×C37C23
cosocleC23×C37C24
hypercenterC23×D4D37
hypocenterC37C2×#386
LCSG ▷ C22×C37 ▷ C37
UCSC1 ◁ C24 ◁ C23×D4

1576 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2368

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 6929);