Finite Group Databasebeta

C4×#11924519 #17997118

order4736
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC4×#11924519

Splittings

FittingC22×C42×C37 ⋊ C2
SylowC37 ⋊ C4×#123

Subgroups

subgroupG/H
centerC22×C4C22×D37
commutatorC22×C37C23×C4
FrattiniC23C23×D37
FittingC22×C42×C37C2
socle, cosocleC23×C37C24
prime radicalC22×C22⋊D37C22
hypercenterC22×C42D37
hypocenterC37C4×#123
LCSG ▷ C22×C37 ▷ C37
UCSC1 ◁ C22×C4 ◁ C22×C42

688 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, 7032);