Finite Group Databasebeta

C22×#11924447 #18003000

order4736
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C26

Aliases

direct productC22×#11924447

Splittings

SylowC37 ⋊ C22×#97

Subgroups

subgroupG/H
centerC23×C4C2×D37
commutatorC2×C37C22×C42
FrattiniC2×C4C23×D37
FittingC22×C42×C37C2
socle, prime radicalC24×C37C2×C4
cosocleC2×C4×C37C24
hypercenterC22×C42D37
hypocenterC37C22×#97
LCSG ▷ C2×C37 ▷ C37
UCSC1 ◁ C23×C4 ◁ C22×C42

680 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4736

Conjugacy classes & character table

1232 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 12914);