Finite Group Databasebeta

C2×#14557913 #18005012

order4736
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C24×C4

Aliases

direct productC2×#14557913

Splittings

SylowC37 ⋊ C2×#494

Subgroups

subgroupG/H
centerC23C2×D148
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC2×C4×C8×C37C2
socle, prime radicalC23×C37C2×D4
hypercenterC2×C4×C8D37
hypocenterC37C2×#494
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×C8

552 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, 14926);