Finite Group Databasebeta

C2×#34039219 #49182749

order37952
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C23

Aliases

direct productC2×#34039219

Splittings

SylowC593 ⋊ C2×#107

Subgroups

subgroupG/H
centerC23D2372
commutatorC4×C593C22×C4
FrattiniC2×C4C22×D593
FittingC22×C8×C593C2
socle, prime radicalC23×C593D4
cosocleC2×C4×C593C23
hypercenterC22×C8D593
hypocenterC593C2×#107
LCSG ▷ C4×C593 ▷ C2×C593 ▷ C593
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8

130 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 37952

Conjugacy classes & character table

9500 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37952, 583);