Finite Group Databasebeta

C2×C22⋊#18011654 #49182676

order37952
automorphism?
homologyAbelianization (H1) = C22×C8 · Schur multiplier (H2) = C24

Aliases

direct productC2×C22⋊#18011654

Splittings

SylowC593 ⋊ C2×C22⋊C8

Subgroups

subgroupG/H
centerC22×C4C2×D593
commutatorC2×C593C22×C8
FrattiniC2×C4C22×D593
FittingC23×C4×C593C2
socleC23×C593C2×C4
prime radicalC24×C593C4
cosocleC2×C4×C593C23
hypercenterC23×C4D593
hypocenterC593C2×C22⋊C8
LCSG ▷ C2×C593 ▷ C593
UCSC1 ◁ C22×C4 ◁ C23×C4

202 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 18976

Conjugacy classes & character table

9512 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37952, 510);