Finite Group Databasebeta

C2×#14557295 #17994309

order4736
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C25

Aliases

direct productC2×#14557295

Splittings

SylowC37 ⋊ C2×#340

Subgroups

subgroupG/H
centerC24C22⋊D37
commutatorC4×C37C2×C42
FrattiniC22×C4C22×D37
FittingC22×C4⋊C4×C37C2
socle, prime radicalC24×C37D4
cosocleC22×C4×C37C23
hypercenterC22×C4⋊C4D37
hypocenterC37C2×#340
LCSG ▷ C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C24 ◁ C23×C4 ◁ C22×C4⋊C4

512 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4736

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 4223);