Finite Group Databasebeta

C2×#34036130 #49167297

order37504
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC2×#34036130

Splittings

SylowC293 ⋊ C2×#417

Subgroups

subgroupG/H
centerC23C2×C22⋊D293
commutatorC4×C293C23×C4
FrattiniC2×C4C23×D293
Fitting, prime radicalC22×#41×C293C2
socleC23×C293C2×D4
cosocleC2×C4×C293C24
hypercenterC22×#41D293
hypocenterC293C2×#417
LCSG ▷ C4×C293 ▷ C2×C293 ▷ C293
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#41

816 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 18752

Conjugacy classes & character table

5884 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37504, 13022);