Finite Group Databasebeta

C2×#19134840 #25097508

order11008
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C27

Aliases

direct productC2×#19134840

Splittings

SylowC43 ⋊ C2×#1862

Subgroups

subgroupG/H
centerC24D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC22×#102×C43C2
socleC24×C43C2×D4
prime radicalC23×D4×C43C22
cosocleC22×C4×C43C24
hypercenterC22×#102D43
hypocenterC43C2×#1862
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C24 ◁ C23×C4 ◁ C22×#102

1974 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1252 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 170479);