Finite Group Databasebeta

C2×#34039220 #49182760

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

Aliases

direct productC2×#34039220

Splittings

SylowC593 ⋊ C2×#108

Subgroups

subgroupG/H
centerC2×C4C22⋊D593
commutatorC4×C593C22×C4
FrattiniC2×C4C22×D593
FittingC2×M16×C593C2
socleC22×C593C4⋊C4
prime radicalC23×C593Q8
cosocleC2×C4×C593C23
hypercenterC2×M16D593
hypocenterC593C2×#108
LCSG ▷ C4×C593 ▷ C2×C593 ▷ C593
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×M16

106 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 18976

Conjugacy classes & character table

5948 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37952, 594);