Finite Group Databasebeta

C2×#14558466 #18011018

order4736
automorphism?
homologyAbelianization (H1) = C22×C16 · Schur multiplier (H2) = C22

Aliases

direct productC2×#14558466

Splittings

SylowC37 ⋊ C2×M64

Subgroups

subgroupG/H
centerC2×C8C2×#3866
commutatorC2×C37C22×C16
FrattiniC8C22×#3866
FittingC2×C16×C37C4
socleC22×C37C2×C16
prime radicalC22×D37C16
cosocle#10596925C23
hypercenterC2×C16#3866
hypocenterC37C2×M64
LCSG ▷ C2×C37 ▷ C37
UCSC1 ◁ C2×C8 ◁ C2×C16

112 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2368

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, 20932);