Finite Group Databasebeta

C2×#14557662 #18003522

order4736
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C24

Aliases

direct productC2×#14557662

Splittings

SylowC37 ⋊ C2×#446

Subgroups

subgroupG/H
centerC22×C4C22×D37
commutatorC22×C37C23×C4
FrattiniC2×C4C23×D37
FittingC2×C4⋊C8×C37C2
socle, prime radicalC23×C37C22×C4
cosocleC2×C4×C37C24
hypercenterC2×C4⋊C8D37
hypocenterC37C2×#446
LCSG ▷ C22×C37 ▷ C37
UCSC1 ◁ C22×C4 ◁ C2×C4⋊C8

400 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, 13436);