Finite Group Databasebeta

C22×#11924468 #18003168

order4736
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC22×#11924468

Splittings

SylowC37 ⋊ C22×#106

Subgroups

subgroupG/H
centerC24D148
commutatorC4×C37C23×C4
FrattiniC2×C4C23×D37
FittingC23×C8×C37C2
socle, prime radicalC24×C37D4
cosocleC2×C4×C37C24
hypercenterC23×C8D37
hypocenterC37C22×#106
LCSG ▷ C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C24 ◁ C23×C4 ◁ C23×C8

600 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4736

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, 13082);