Finite Group Databasebeta

C2×#14557534 #18003108

order4736
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC2×#14557534

Splittings

SylowC37 ⋊ C2×#417

Subgroups

subgroupG/H
centerC23C2×C22⋊D37
commutatorC4×C37C23×C4
FrattiniC2×C4C23×D37
Fitting, prime radicalC22×#41×C37C2
socleC23×C37C2×D4
cosocleC2×C4×C37C24
hypercenterC22×#41D37
hypocenterC37C2×#417
LCSG ▷ C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#41

816 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2368

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 13022);