Finite Group Databasebeta

C2×#20242191 #26185644

order12032
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C25

Aliases

direct productC2×#20242191

Splittings

SylowC47 ⋊ C2×C8×SD16

Subgroups

subgroupG/H
centerC22×C4D4×D47
commutatorC4×C47C23×C8
FrattiniC42C23×D47
FittingC2×C47×D4⋊C8C2
socleC23×C47C4×D4
prime radicalC22×D4×C47C2×C4
cosocleC42×C47C24
hypercenterC2×D4⋊C8D47
hypocenterC47C2×C8×SD16
LCSG ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×D4⋊C8

822 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1400 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 138934);