Finite Group Databasebeta

C2×#20242825 #26198571

order12032
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C25

Aliases

direct productC2×#20242825

Splittings

FittingC2×C8×D4×C47 ⋊ C2
SylowC47 ⋊ C2×#1681

Subgroups

subgroupG/H
centerC23#13093998
commutator, cosocleC42×C47C24
FrattiniC42C23×D47
FittingC2×C8×D4×C47C2
socleC23×C47#121
prime radicalC2×#15689318C2
hypercenterC2×C8×D4D47
hypocenterC47C2×#1681
LCSG ▷ C42×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C8×D4

842 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1898 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 151861);