Finite Group Databasebeta

C2×#19134420 #25094354

order11008
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C26×C4

Aliases

direct productC2×#19134420

Splittings

SylowC43 ⋊ C2×#1762

Subgroups

subgroupG/H
centerC24C2×C22⋊D43
commutatorC4×C43C22×C42
FrattiniC22×C4C23×D43
FittingC22×C4×D4×C43C2
socleC24×C43C2×D4
prime radicalC23×D4×C43C22
cosocleC22×C4×C43C24
hypercenterC22×C4×D4D43
hypocenterC43C2×#1762
LCSG ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C24 ◁ C22×C42 ◁ C22×C4×D4

2118 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1768 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 167325);