Finite Group Databasebeta

C2×#20243336 #26215538

order12032
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C29

Aliases

direct productC2×#20243336

Splittings

SylowC47 ⋊ C2×#1790

Subgroups

subgroupG/H
centerC23#13093993
commutatorC23×C47C23×C4
FrattiniC24C23×D47
Fitting, prime radicalC22×H(5,𝔽2)×C47C2
socleC23×C47#120
cosocleC24×C47C24
hypercenterC22×H(5,𝔽2)D47
hypocenterC47C2×#1790
LCSG ▷ C23×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C25 ◁ C22×H(5,𝔽2)

4402 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1628 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 168828);