Finite Group Databasebeta

C2×#14558399 #18010256

order4736
automorphism?
homologyAbelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C25

Aliases

direct productC2×#14558399

Splittings

SylowC37 ⋊ C2×#336

Subgroups

subgroupG/H
centerC24C2×#3866
commutatorC2×C37C2×C4×C8
FrattiniC23C22×#3866
FittingC23×C4×C37C4
socle, prime radicalC24×C37C2×C4
cosocleC22×Dic37C23
hypercenterC23×C4#3866
hypocenterC37C2×#336
LCSG ▷ C2×C37 ▷ C37
UCSC1 ◁ C24 ◁ C23×C4

528 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, 20170);