Finite Group Databasebeta

C2×#14557560 #18003155

order4736
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC2×#14557560

Splittings

SylowC37 ⋊ C2×#424

Subgroups

subgroupG/H
centerC22×C4C22×D37
commutatorC22×C37C23×C4
FrattiniC2×C4C23×D37
FittingC2×#117×C37C2
socleC23×C37C22×C4
prime radicalC24×C37C2×C4
cosocleC2×C4×C37C24
hypercenterC2×#117D37
hypocenterC37C2×#424
LCSG ▷ C22×C37 ▷ C37
UCSC1 ◁ C22×C4 ◁ C2×#117

512 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2368

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, 13069);