Finite Group Databasebeta

C2×#14558408 #18010286

order4736
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C24

Aliases

direct productC2×#14558408

Splittings

SylowC37 ⋊ C2×#341

Subgroups

subgroupG/H
centerC2×C4C22⋊#3866
commutatorC4×C37C2×C42
FrattiniC2×C4C22×#3866
FittingC2×M16×C37C4
socleC22×C37#95
prime radicalC23×D37Q8
cosocleC2×C4×D37C23
hypercenterC2×M16#3866
hypocenterC37C2×#341
LCSG ▷ C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×M16

392 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1184

Conjugacy classes & character table

236 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 20200);