Finite Group Databasebeta

C22×Dic296 #18007709

order4736
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C25

Aliases

direct productC22×Dic296

Splittings

SylowC37 ⋊ C22×Q32

Subgroups

subgroupG/H
centerC23D296
commutator, cosocleC8×C37C24
FrattiniC8C23×D37
FittingC22×C16×C37C2
socle, prime radicalC23×C37D8
hypercenterC22×C16D37
hypocenterC37C22×Q32
LCSG ▷ C8×C37 ▷ C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8 ◁ C22×C16

360 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4736

Conjugacy classes & character table

1196 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 17623);