Finite Group Databasebeta

C2×#14558374 #18009789

order4736
automorphism?
homologyAbelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C22×C4

Aliases

direct productC2×#14558374

Splittings

SylowC37 ⋊ C2×#322

Subgroups

subgroupG/H
centerC22×C4C2×#3866
commutatorC2×C37C2×C4×C8
FrattiniC2×C4C22×#3866
FittingC22×C8×C37C4
socle, prime radicalC23×C37C42
cosocleC4×Dic37C23
hypercenterC22×C8#3866
hypocenterC37C2×#322
LCSG ▷ C2×C37 ▷ C37
UCSC1 ◁ C22×C4 ◁ C22×C8

248 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4736

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 19703);