Finite Group Databasebeta

C2×C4×#13063313 #25255070

order11008
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C28×C4

Aliases

direct productC2×C4×#13063313

Splittings

FittingC2×C43×C43 ⋊ C2
SylowC43 ⋊ C2×C4×#124

Subgroups

subgroupG/H
centerC23×C4C22×D43
commutatorC22×C43C24×C4
FrattiniC23C24×D43
FittingC2×C43×C43C2
socleC24×C43C24
prime radicalC23×D172C22
cosocleC23×C43C25
hypercenterC2×C43D43
hypocenterC43C2×C4×#124
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C23×C4 ◁ C2×C43

3790 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2800 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 328041);