Finite Group Databasebeta

C2×#14558461 #18010949

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

Aliases

direct productC2×#14558461

Splittings

SylowC37 ⋊ C2×#368

Subgroups

subgroupG/H
centerC22#11924605
commutatorC8×C37C22×C4
FrattiniC8C22×#3866
FittingC2×C16×C37C4
socleC22×C37#107
prime radicalC22×D37Q16
cosocleC8×D37C23
hypercenterC2×C16#3866
hypocenterC37C2×#368
LCSG ▷ C8×C37 ▷ C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16

144 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2368

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 20863);