Finite Group Databasebeta

C2×#20247153 #26384177

order12032
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C29

Aliases

direct productC2×#20247153

Splittings

FittingC2×C4×C4⋊C4×C47 ⋊ C2
SylowC47 ⋊ C2×#2445

Subgroups

subgroupG/H
centerC24C23×D47
commutator, cosocleC23×C47C25
FrattiniC23C24×D47
FittingC2×C4×C4⋊C4×C47C2
socleC24×C47C24
prime radicalC22×#13094021C2
hypercenterC2×C4×C4⋊C4D47
hypocenterC47C2×#2445
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C24 ◁ C2×C4×C4⋊C4

4110 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1916 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 337467);